视频数据可视化

视频标题	中文标题	视频列表标题	中文视频列表标题	作者	原始链接
This tests your understanding of light \| The barber pole effect		Optics puzzles		3Blue1Brown	原始链接
How wiggling charges give rise to light		Optics puzzles		3Blue1Brown	原始链接
But why would light "slow down"? \| Visualizing Feynman's lecture on the refractive index		Optics puzzles		3Blue1Brown	原始链接
Answering viewer questions about refraction		Optics puzzles		3Blue1Brown	原始链接
How are holograms possible?		Optics puzzles		3Blue1Brown	原始链接
But what is the Central Limit Theorem?		Central limit theorem		3Blue1Brown	原始链接
Why π is in the normal distribution (beyond integral tricks)		Central limit theorem		3Blue1Brown	原始链接
Convolutions \| Why X+Y in probability is a beautiful mess		Central limit theorem		3Blue1Brown	原始链接
A pretty reason why Gaussian + Gaussian = Gaussian		Central limit theorem		3Blue1Brown	原始链接
Convolutions in Image Processing \| Week 1, lecture 6 \| MIT 18.S191 Fall 2020		Selected lectures on computational thinking for MIT 18.S191		The Julia Programming Language	原始链接
Seam Carving \| Week 2, lecture 7 \| 18.S191 MIT Fall 2020		Selected lectures on computational thinking for MIT 18.S191		The Julia Programming Language	原始链接
The diffusion equation \| Week 12 \| MIT 18.S191 Fall 2020 \| Grant Sanderson		Selected lectures on computational thinking for MIT 18.S191		The Julia Programming Language	原始链接
What is a Discrete Fourier Transform? \| Week 14 \| MIT 18.S191 Fall 2020 \| Grant Sanderson		Selected lectures on computational thinking for MIT 18.S191		The Julia Programming Language	原始链接
Exponential growth and epidemics		COVID-19		3Blue1Brown	原始链接
Simulating an epidemic		COVID-19		3Blue1Brown	原始链接
The DP-3T algorithm for contact tracing (with Nicky Case)		COVID-19		3Blue1Brown	原始链接
Lockdown math announcement		Lockdown math		3Blue1Brown	原始链接
The simpler quadratic formula \| Ep. 1 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
Trigonometry fundamentals \| Ep. 2 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
Complex number fundamentals \| Ep. 3 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
What is Euler's formula actually saying? \| Ep. 4 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
Imaginary interest rates \| Ep. 5 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
Logarithm Fundamentals \| Ep. 6 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
What makes the natural log "natural"? \| Ep. 7 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
The power tower puzzle \| Ep. 8 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
Intuition for i to the power i \| Ep. 9 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
Tips to be a better problem solver [Last live lecture] \| Ep. 10 Lockdown live math		Lockdown math		3Blue1Brown	原始链接
Binomial distributions \| Probabilities of probabilities, part 1		Probabilities of probabilities		3Blue1Brown	原始链接
Why “probability of 0” does not mean “impossible” \| Probabilities of probabilities, part 2		Probabilities of probabilities		3Blue1Brown	原始链接
Deep Dive into LLMs like ChatGPT				Andrej Karpathy	原始链接
How I use LLMs				Andrej Karpathy	原始链接
NotebookLM Will Change How You Learn – Here’s Why!				Tiago Forte	原始链接
Lecture 52: Scaling Laws for Low Precision		GPU MODE - Videos		GPU MODE	原始链接
Lecture 51: Consumer GPU performance		GPU MODE - Videos		GPU MODE	原始链接
Lecture 50: A learning journey CUDA, Triton, Flash Attention		GPU MODE - Videos		GPU MODE	原始链接
Lecture 48: The Ultra Scale Playbook		GPU MODE - Videos		GPU MODE	原始链接
Lecture 49: Low Bit Metal Kernels		GPU MODE - Videos		GPU MODE	原始链接
Lecture 47: KernelBot Benchmark GPU Kernels on Discord		GPU MODE - Videos		GPU MODE	原始链接
Lecture 46: Distributed GEMM		GPU MODE - Videos		GPU MODE	原始链接
Lecture 44: NVIDIA Profiling		GPU MODE - Videos		GPU MODE	原始链接
Lecture 45: Outperforming cuBLAS on H100		GPU MODE - Videos		GPU MODE	原始链接
Lecture 43: int8 tensorcore matmul for Turing		GPU MODE - Videos		GPU MODE	原始链接
Lecture 42: Mosaic GPU		GPU MODE - Videos		GPU MODE	原始链接
Lecture 41: FlashInfer		GPU MODE - Videos		GPU MODE	原始链接
Lecture 40: CUDA Docs for Humans		GPU MODE - Videos		GPU MODE	原始链接
Lecture 39: Torchtitan		GPU MODE - Videos		GPU MODE	原始链接
Lecture 38: Low Bit ARM kernels		GPU MODE - Videos		GPU MODE	原始链接
Lecture 37: Introduction to SASS & GPU Microarchitecture		GPU MODE - Videos		GPU MODE	原始链接
Lecture 36: CUTLASS and Flash Attention 3		GPU MODE - Videos		GPU MODE	原始链接
Lecture 35: SGLang		GPU MODE - Videos		GPU MODE	原始链接
Lecture 34: Low Bit Triton Kernels		GPU MODE - Videos		GPU MODE	原始链接
Lecture 33: Bitblas		GPU MODE - Videos		GPU MODE	原始链接
Lecture 32: Unsloth		GPU MODE - Videos		GPU MODE	原始链接
Lecture 31: Beginners Guide to Metal		GPU MODE - Videos		GPU MODE	原始链接
The History of CUDA MODE (Now GPU MODE)		GPU MODE - Videos		GPU MODE	原始链接
Lecture 30: Quantized Training		GPU MODE - Videos		GPU MODE	原始链接
GPU MODE IRL 2024 Keynotes		GPU MODE - Videos		GPU MODE	原始链接
Lecture 29: Triton Internals		GPU MODE - Videos		GPU MODE	原始链接
Lecture 28: Liger Kernel - Efficient Triton Kernels for LLM Training		GPU MODE - Videos		GPU MODE	原始链接
Lecture 27: gpu.cpp - Portable GPU compute using WebGPU		GPU MODE - Videos		GPU MODE	原始链接
Lecture 26: SYCL Mode (Intel GPU)		GPU MODE - Videos		GPU MODE	原始链接
Lecture 25: Speaking Composable Kernel (CK)		GPU MODE - Videos		GPU MODE	原始链接
Lecture 24: Scan at the Speed of Light		GPU MODE - Videos		GPU MODE	原始链接
Lecture 23: Tensor Cores		GPU MODE - Videos		GPU MODE	原始链接
Lecture 22: Hacker's Guide to Speculative Decoding in VLLM		GPU MODE - Videos		GPU MODE	原始链接
Lecture 21: Scan Algorithm Part 2		GPU MODE - Videos		GPU MODE	原始链接
Lecture 20: Scan Algorithm		GPU MODE - Videos		GPU MODE	原始链接
Lecture 19: Data Processing on GPUs		GPU MODE - Videos		GPU MODE	原始链接
Lecture 18: Fusing Kernels		GPU MODE - Videos		GPU MODE	原始链接
Lecture 17: NCCL		GPU MODE - Videos		GPU MODE	原始链接
Lecture 16: On Hands Profiling		GPU MODE - Videos		GPU MODE	原始链接
Bonus Lecture: CUDA C++ llm.cpp		GPU MODE - Videos		GPU MODE	原始链接
Lecture 15: CUTLASS		GPU MODE - Videos		GPU MODE	原始链接
Lecture 14: Practitioners Guide to Triton		GPU MODE - Videos		GPU MODE	原始链接
Lecture 13: Ring Attention		GPU MODE - Videos		GPU MODE	原始链接
Lecture 12: Flash Attention		GPU MODE - Videos		GPU MODE	原始链接
Lecture 11: Sparsity		GPU MODE - Videos		GPU MODE	原始链接
Lecture 10: Build a Prod Ready CUDA library		GPU MODE - Videos		GPU MODE	原始链接
Lecture 9 Reductions		GPU MODE - Videos		GPU MODE	原始链接
Lecture 8: CUDA Performance Checklist		GPU MODE - Videos		GPU MODE	原始链接
Lecture 7 Advanced Quantization		GPU MODE - Videos		GPU MODE	原始链接
Lecture 6 Optimizing Optimizers		GPU MODE - Videos		GPU MODE	原始链接
Lecture 5: Going Further with CUDA for Python Programmers		GPU MODE - Videos		GPU MODE	原始链接
Lecture 4 Compute and Memory Basics		GPU MODE - Videos		GPU MODE	原始链接
Lecture 3: Getting Started With CUDA for Python Programmers		GPU MODE - Videos		GPU MODE	原始链接
Lecture 2 Ch1-3 PMPP book		GPU MODE - Videos		GPU MODE	原始链接
Lecture 1 How to profile CUDA kernels in PyTorch		GPU MODE - Videos		GPU MODE	原始链接
There's more to those colliding blocks that compute pi		3Blue1Brown - Videos		3Blue1Brown	原始链接
How to measure the universe \| The Cosmic Distance Ladder Part 2		3Blue1Brown - Videos		3Blue1Brown	原始链接
Terence Tao on how we measure the cosmos \| The Distance Ladder Part 1		3Blue1Brown - Videos		3Blue1Brown	原始链接
This open problem taught me what topology is		3Blue1Brown - Videos		3Blue1Brown	原始链接
Large Language Models explained briefly		3Blue1Brown - Videos		3Blue1Brown	原始链接
Five puzzles for thinking outside the box		3Blue1Brown - Videos		3Blue1Brown	原始链接
How I animate 3Blue1Brown \| A Manim demo with Ben Sparks		3Blue1Brown - Videos		3Blue1Brown	原始链接
How might LLMs store facts \| DL7		3Blue1Brown - Videos		3Blue1Brown	原始链接
What "Follow Your Dreams" Misses \| Harvey Mudd Commencement Speech 2024		3Blue1Brown - Videos		3Blue1Brown	原始链接
Attention in transformers, step-by-step \| DL6		3Blue1Brown - Videos		3Blue1Brown	原始链接
Transformers (how LLMs work) explained visually \| DL5		3Blue1Brown - Videos		3Blue1Brown	原始链接
25 Math explainers you may enjoy \| SoME3 results		3Blue1Brown - Videos		3Blue1Brown	原始链接
This pattern breaks, but for a good reason \| Moser's circle problem		3Blue1Brown - Videos		3Blue1Brown	原始链接
How They Fool Ya (live) \| Math parody of Hallelujah		3Blue1Brown - Videos		3Blue1Brown	原始链接
But what is a convolution?		3Blue1Brown - Videos		3Blue1Brown	原始链接
Researchers thought this was a bug (Borwein integrals)		3Blue1Brown - Videos		3Blue1Brown	原始链接
What makes a great math explanation? \| SoME2 results		3Blue1Brown - Videos		3Blue1Brown	原始链接
How to lie using visual proofs		3Blue1Brown - Videos		3Blue1Brown	原始链接
Olympiad level counting (Generating functions)		3Blue1Brown - Videos		3Blue1Brown	原始链接
Oh, wait, actually the best Wordle opener is not “crane”…		3Blue1Brown - Videos		3Blue1Brown	原始链接
Solving Wordle using information theory		3Blue1Brown - Videos		3Blue1Brown	原始链接
A tale of two problem solvers \| Average cube shadow area		3Blue1Brown - Videos		3Blue1Brown	原始链接
2021 Summer of Math Exposition results		3Blue1Brown - Videos		3Blue1Brown	原始链接
Beyond the Mandelbrot set, an intro to holomorphic dynamics		3Blue1Brown - Videos		3Blue1Brown	原始链接
Newton’s fractal (which Newton knew nothing about)		3Blue1Brown - Videos		3Blue1Brown	原始链接
Make math videos! \| Summer of Math Exposition announcement		3Blue1Brown - Videos		3Blue1Brown	原始链接
A quick trick for computing eigenvalues \| Chapter 15, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
How (and why) to raise e to the power of a matrix \| DE6		3Blue1Brown - Videos		3Blue1Brown	原始链接
The medical test paradox, and redesigning Bayes' rule		3Blue1Brown - Videos		3Blue1Brown	原始链接
Hamming codes part 2: The one-line implementation		3Blue1Brown - Videos		3Blue1Brown	原始链接
But what are Hamming codes? The origin of error correction		3Blue1Brown - Videos		3Blue1Brown	原始链接
Group theory, abstraction, and the 196,883-dimensional monster		3Blue1Brown - Videos		3Blue1Brown	原始链接
The impossible chessboard puzzle		3Blue1Brown - Videos		3Blue1Brown	原始链接
The quick proof of Bayes' theorem		3Blue1Brown - Videos		3Blue1Brown	原始链接
Bayes theorem, the geometry of changing beliefs		3Blue1Brown - Videos		3Blue1Brown	原始链接
Q&A with Grant, windy walk edition		3Blue1Brown - Videos		3Blue1Brown	原始链接
Why do prime numbers make these spirals? \| Dirichlet’s theorem and pi approximations		3Blue1Brown - Videos		3Blue1Brown	原始链接
The unexpectedly hard windmill question (2011 IMO, Q2)		3Blue1Brown - Videos		3Blue1Brown	原始链接
e^(iπ) in 3.14 minutes, using dynamics \| DE5		3Blue1Brown - Videos		3Blue1Brown	原始链接
Pure Fourier series animation montage		3Blue1Brown - Videos		3Blue1Brown	原始链接
But what is a Fourier series? From heat flow to drawing with circles \| DE4		3Blue1Brown - Videos		3Blue1Brown	原始链接
Solving the heat equation \| DE3		3Blue1Brown - Videos		3Blue1Brown	原始链接
But what is a partial differential equation? \| DE2		3Blue1Brown - Videos		3Blue1Brown	原始链接
Differential equations, a tourist's guide \| DE1		3Blue1Brown - Videos		3Blue1Brown	原始链接
Cramer's rule, explained geometrically \| Chapter 12, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
How colliding blocks act like a beam of light...to compute pi.		3Blue1Brown - Videos		3Blue1Brown	原始链接
The most unexpected answer to a counting puzzle		3Blue1Brown - Videos		3Blue1Brown	原始链接
But why is a sphere's surface area four times its shadow?		3Blue1Brown - Videos		3Blue1Brown	原始链接
Using topology for discrete problems \| The Borsuk-Ulam theorem and stolen necklaces		3Blue1Brown - Videos		3Blue1Brown	原始链接
Why 5/3 is a fundamental constant for turbulence		3Blue1Brown - Videos		3Blue1Brown	原始链接
Quaternions and 3d rotation, explained interactively		3Blue1Brown - Videos		3Blue1Brown	原始链接
Visualizing quaternions (4d numbers) with stereographic projection		3Blue1Brown - Videos		3Blue1Brown	原始链接
Q&A with Grant Sanderson (3blue1brown)		3Blue1Brown - Videos		3Blue1Brown	原始链接
Why slicing a cone gives an ellipse (beautiful proof)		3Blue1Brown - Videos		3Blue1Brown	原始链接
Other math channels you'd enjoy		3Blue1Brown - Videos		3Blue1Brown	原始链接
Divergence and curl: The language of Maxwell's equations, fluid flow, and more		3Blue1Brown - Videos		3Blue1Brown	原始链接
The other way to visualize derivatives \| Chapter 12, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
The Wallis product for pi, proved geometrically		3Blue1Brown - Videos		3Blue1Brown	原始链接
Winding numbers and domain coloring		3Blue1Brown - Videos		3Blue1Brown	原始链接
How pi was almost 6.283185...		3Blue1Brown - Videos		3Blue1Brown	原始链接
Why is pi here? And why is it squared? A geometric answer to the Basel problem		3Blue1Brown - Videos		3Blue1Brown	原始链接
The more general uncertainty principle, regarding Fourier transforms		3Blue1Brown - Videos		3Blue1Brown	原始链接
But what is the Fourier Transform? A visual introduction.		3Blue1Brown - Videos		3Blue1Brown	原始链接
Why this puzzle is impossible		3Blue1Brown - Videos		3Blue1Brown	原始链接
Q&A #2 + Net Neutrality Nuance		3Blue1Brown - Videos		3Blue1Brown	原始链接
The hardest problem on the hardest test		3Blue1Brown - Videos		3Blue1Brown	原始链接
Backpropagation calculus \| DL4		3Blue1Brown - Videos		3Blue1Brown	原始链接
Backpropagation, intuitively \| DL3		3Blue1Brown - Videos		3Blue1Brown	原始链接
Gradient descent, how neural networks learn \| DL2		3Blue1Brown - Videos		3Blue1Brown	原始链接
But what is a neural network? \| Deep learning chapter 1		3Blue1Brown - Videos		3Blue1Brown	原始链接
Some light quantum mechanics (with minutephysics)		3Blue1Brown - Videos		3Blue1Brown	原始链接
Thinking outside the 10-dimensional box		3Blue1Brown - Videos		3Blue1Brown	原始链接
Hilbert's Curve: Is infinite math useful?		3Blue1Brown - Videos		3Blue1Brown	原始链接
How secure is 256 bit security?		3Blue1Brown - Videos		3Blue1Brown	原始链接
But how does bitcoin actually work?		3Blue1Brown - Videos		3Blue1Brown	原始链接
All possible pythagorean triples, visualized		3Blue1Brown - Videos		3Blue1Brown	原始链接
Pi hiding in prime regularities		3Blue1Brown - Videos		3Blue1Brown	原始链接
Taylor series \| Chapter 11, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
Higher order derivatives \| Chapter 10, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
What does area have to do with slope? \| Chapter 9, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
Integration and the fundamental theorem of calculus \| Chapter 8, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
Limits, L'Hôpital's rule, and epsilon delta definitions \| Chapter 7, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
Implicit differentiation, what's going on here? \| Chapter 6, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
What's so special about Euler's number e? \| Chapter 5, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
Visualizing the chain rule and product rule \| Chapter 4, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
Derivative formulas through geometry \| Chapter 3, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
The paradox of the derivative \| Chapter 2, Essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
The essence of calculus		3Blue1Brown - Videos		3Blue1Brown	原始链接
Euler's formula with introductory group theory		3Blue1Brown - Videos		3Blue1Brown	原始链接
Fractals are typically not self-similar		3Blue1Brown - Videos		3Blue1Brown	原始链接
Tattoos on Math		3Blue1Brown - Videos		3Blue1Brown	原始链接
But what is the Riemann zeta function? Visualizing analytic continuation		3Blue1Brown - Videos		3Blue1Brown	原始链接
Binary, Hanoi, and Sierpinski, part 2		3Blue1Brown - Videos		3Blue1Brown	原始链接
Binary, Hanoi and Sierpinski, part 1		3Blue1Brown - Videos		3Blue1Brown	原始链接
3blue1brown channel trailer		3Blue1Brown - Videos		3Blue1Brown	原始链接
Who cares about topology? (Old version)		3Blue1Brown - Videos		3Blue1Brown	原始链接
Abstract vector spaces \| Chapter 16, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Eigenvectors and eigenvalues \| Chapter 14, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Change of basis \| Chapter 13, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Cross products \| Chapter 10, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Cross products in the light of linear transformations \| Chapter 11, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Dot products and duality \| Chapter 9, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Nonsquare matrices as transformations between dimensions \| Chapter 8, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Inverse matrices, column space and null space \| Chapter 7, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
The determinant \| Chapter 6, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Three-dimensional linear transformations \| Chapter 5, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Matrix multiplication as composition \| Chapter 4, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Linear transformations and matrices \| Chapter 3, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Linear combinations, span, and basis vectors \| Chapter 2, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Vectors \| Chapter 1, Essence of linear algebra		3Blue1Brown - Videos		3Blue1Brown	原始链接
Essence of linear algebra preview		3Blue1Brown - Videos		3Blue1Brown	原始链接
Triangle of Power		3Blue1Brown - Videos		3Blue1Brown	原始链接
Snell's law proof using springs		3Blue1Brown - Videos		3Blue1Brown	原始链接
The Brachistochrone, with Steven Strogatz		3Blue1Brown - Videos		3Blue1Brown	原始链接
Fractal charm: Space filling curves		3Blue1Brown - Videos		3Blue1Brown	原始链接
Music And Measure Theory		3Blue1Brown - Videos		3Blue1Brown	原始链接
How to count to 1000 on two hands		3Blue1Brown - Videos		3Blue1Brown	原始链接
What does it feel like to invent math?		3Blue1Brown - Videos		3Blue1Brown	原始链接
Euler's Formula and Graph Duality		3Blue1Brown - Videos		3Blue1Brown	原始链接
Euler's Formula Poem		3Blue1Brown - Videos		3Blue1Brown	原始链接
e to the pi i, a nontraditional take (old version)		3Blue1Brown - Videos		3Blue1Brown	原始链接
I finally find least action principle satisfying		Mathemaniac - Videos		Mathemaniac	原始链接
The most important theorem in (differential) geometry \| Euler characteristic #3		Mathemaniac - Videos		Mathemaniac	原始链接
7-colour theorem on the torus \| Euler characteristic #2		Mathemaniac - Videos		Mathemaniac	原始链接
The "textbook exercise" on Euler characteristic \| Euler characteristic #1		Mathemaniac - Videos		Mathemaniac	原始链接
How physics solves a math problem (and a 3D graphics problem)		Mathemaniac - Videos		Mathemaniac	原始链接
The clever way curvature is described in math		Mathemaniac - Videos		Mathemaniac	原始链接
Lie algebras visualized: why are they defined like that? Why Jacobi identity?		Mathemaniac - Videos		Mathemaniac	原始链接
Matrix trace isn't just summing the diagonal \| Lie groups, algebras, brackets #5		Mathemaniac - Videos		Mathemaniac	原始链接
Can we exponentiate d/dx? Vector (fields)? What is exp? \| Lie groups, algebras, brackets #4		Mathemaniac - Videos		Mathemaniac	原始链接
What is Lie theory? Here is the big picture. \| Lie groups, algebras, brackets #3		Mathemaniac - Videos		Mathemaniac	原始链接
How to rotate in higher dimensions? Complex dimensions? \| Lie groups, algebras, brackets #2		Mathemaniac - Videos		Mathemaniac	原始链接
Why study Lie theory? \| Lie groups, algebras, brackets #1		Mathemaniac - Videos		Mathemaniac	原始链接
How many terms do we need in the exp series?		Mathemaniac - Videos		Mathemaniac	原始链接
Queuing theory and Poisson process		Mathemaniac - Videos		Mathemaniac	原始链接
Theorema Egregium: why all maps are wrong		Mathemaniac - Videos		Mathemaniac	原始链接
The biggest misconception about spin 1/2		Mathemaniac - Videos		Mathemaniac	原始链接
I use PowerPoint to edit all* videos (and hit 100k subs!)		Mathemaniac - Videos		Mathemaniac	原始链接
The deeper meaning of matrix transpose		Mathemaniac - Videos		Mathemaniac	原始链接
How hard was my Cambridge interview? (ft. @TomRocksMaths)		Mathemaniac - Videos		Mathemaniac	原始链接
Random walks in 2D and 3D are fundamentally different (Markov chains approach)		Mathemaniac - Videos		Mathemaniac	原始链接
The weirdest paradox in statistics (and machine learning)		Mathemaniac - Videos		Mathemaniac	原始链接
Why you can't solve quintic equations (Galois theory approach) #SoME2		Mathemaniac - Videos		Mathemaniac	原始链接
The simplest reason why π/4 = 1 - 1/3 + 1/5 -...		Mathemaniac - Videos		Mathemaniac	原始链接
The geometric interpretation of sin x = x - x³/3! + x⁵/5! -...		Mathemaniac - Videos		Mathemaniac	原始链接
Complex integration, Cauchy and residue theorems \| Essence of Complex Analysis #6		Mathemaniac - Videos		Mathemaniac	原始链接
What if we define 1/0 = ∞? \| Möbius transformations visualized		Mathemaniac - Videos		Mathemaniac	原始链接
What do complex functions look like? \| Essence of complex analysis #4		Mathemaniac - Videos		Mathemaniac	原始链接
The 5 ways to visualize complex functions \| Essence of complex analysis #3		Mathemaniac - Videos		Mathemaniac	原始链接
What are complex numbers? \| Essence of complex analysis #2		Mathemaniac - Videos		Mathemaniac	原始链接
Why care about complex analysis? \| Essence of complex analysis #1		Mathemaniac - Videos		Mathemaniac	原始链接
Green's functions: the genius way to solve DEs		Mathemaniac - Videos		Mathemaniac	原始链接
From miller to entering Cambridge at age 40 - George Green		Mathemaniac - Videos		Mathemaniac	原始链接
Solved simply: the impossible integral		Mathemaniac - Videos		Mathemaniac	原始链接
What is Jacobian? \| The right way of thinking derivatives and integrals		Mathemaniac - Videos		Mathemaniac	原始链接
The numerical simulation is NOT as easy as you think! - Average distance #2		Mathemaniac - Videos		Mathemaniac	原始链接
Dream cheating scandal - explaining ALL the math simply		Mathemaniac - Videos		Mathemaniac	原始链接
What is the average distance of two points in a disc? (PART 1)		Mathemaniac - Videos		Mathemaniac	原始链接
Icosahedral symmetry - conjugacy classes and simplicity		Mathemaniac - Videos		Mathemaniac	原始链接
Without integration, why is the volume of a paraboloid half of its inscribing cylinder? (DIw/oI #8)		Mathemaniac - Videos		Mathemaniac	原始链接
Problem of Apollonius - what does it teach us about problem solving?		Mathemaniac - Videos		Mathemaniac	原始链接
Burnside's Lemma (Part 2) - combining math, science and music		Mathemaniac - Videos		Mathemaniac	原始链接
Burnside's Lemma (Part 1) - combining group theory and combinatorics		Mathemaniac - Videos		Mathemaniac	原始链接
Limitations of mathematical models; historical context of BGW process [PART III]		Mathemaniac - Videos		Mathemaniac	原始链接
How likely is coronavirus (COVID-19) eradicated? [PART II]		Mathemaniac - Videos		Mathemaniac	原始链接
Alternative to SIR: Modelling coronavirus (COVID-19) with stochastic process [PART I]		Mathemaniac - Videos		Mathemaniac	原始链接
Summary: an example covering ALL group theory concepts!! \| Essence of Group Theory		Mathemaniac - Videos		Mathemaniac	原始链接
Chapter 7: Group actions, symmetric group and Cayley’s theorem \| Essence of Group Theory		Mathemaniac - Videos		Mathemaniac	原始链接
Two opposite games involving golden ratio (ft. Tom Rocks Maths)		Mathemaniac - Videos		Mathemaniac	原始链接
Chapter 6: Homomorphism and (first) isomorphism theorem \| Essence of Group Theory		Mathemaniac - Videos		Mathemaniac	原始链接
Chapter 5: Quotient groups \| Essence of Group Theory		Mathemaniac - Videos		Mathemaniac	原始链接
How will the COVID-19 (coronavirus) epidemic end?		Mathemaniac - Videos		Mathemaniac	原始链接
Chapter 4: Conjugation, normal subgroups and simple groups \| Essence of Group Theory		Mathemaniac - Videos		Mathemaniac	原始链接
Chapter 3: Lagrange's theorem, Subgroups and Cosets \| Essence of Group Theory		Mathemaniac - Videos		Mathemaniac	原始链接
Chapter 2: Orbit-Stabiliser Theorem \| Essence of Group Theory		Mathemaniac - Videos		Mathemaniac	原始链接
Chapter 1: Symmetries, Groups and Actions \| Essence of Group Theory		Mathemaniac - Videos		Mathemaniac	原始链接
Power rule of integrals not using integration; definition of e \| DIw/oI #7		Mathemaniac - Videos		Mathemaniac	原始链接
How do I love math? (Part II - Proof without words)		Mathemaniac - Videos		Mathemaniac	原始链接
How is pi calculated to trillions of digits?		Mathemaniac - Videos		Mathemaniac	原始链接
Why does R(4,4)=18?		Mathemaniac - Videos		Mathemaniac	原始链接
Proof of Ramsey's theorem		Mathemaniac - Videos		Mathemaniac	原始链接
Rhapsody on Ramsey numbers (and aliens?)		Mathemaniac - Videos		Mathemaniac	原始链接
15-year-old did mathematical research?! What was my thinking process back then?		Mathemaniac - Videos		Mathemaniac	原始链接
The art of generalization in Mathematics \| DDC #4		Mathemaniac - Videos		Mathemaniac	原始链接
More ways of deriving Catalan numbers \| DDC #3		Mathemaniac - Videos		Mathemaniac	原始链接
Catalan numbers are not in Catalan \| DDC #2		Mathemaniac - Videos		Mathemaniac	原始链接
Crash Course in Combinatorics \| DDC #1		Mathemaniac - Videos		Mathemaniac	原始链接
Deep Dive into Combinatorics (Introduction)		Mathemaniac - Videos		Mathemaniac	原始链接
A mistake that is not wrong \| Shorts #3		Mathemaniac - Videos		Mathemaniac	原始链接
What is mathematical elegance? How do I love math? \| Shorts #2		Mathemaniac - Videos		Mathemaniac	原始链接
Using physics to compute integrals \| DIw/oI #5		Mathemaniac - Videos		Mathemaniac	原始链接
Indefinite integrals? Cavalieri’s quadrature? Complex analysis? \| DIw/oI #6		Mathemaniac - Videos		Mathemaniac	原始链接
Ancient Greeks (Archimedes) almost discovered calculus! \| DIw/oI #4		Mathemaniac - Videos		Mathemaniac	原始链接
Algebra vs Geometry in Trigonometry \| DIw/oI #3		Mathemaniac - Videos		Mathemaniac	原始链接
We can compute the integral of sine geometrically? \| DIw/oI #2		Mathemaniac - Videos		Mathemaniac	原始链接
Doing integrals without integration (Part I)	不用积分法计算积分（第一部分）	Mathemaniac - Videos	Mathemaniac - 视频	Mathemaniac	原始链接
What is the next term of a sequence? \| Shorts #1		Mathemaniac - Videos		Mathemaniac	原始链接
Everything you need to know about operations in modular arithmetic		Mathemaniac - Videos		Mathemaniac	原始链接
Untold connection: Lagrange and ancient Chinese problem		Mathemaniac - Videos		Mathemaniac	原始链接
Finding Fibonacci general term using LINEAR ALGEBRA		Mathemaniac - Videos		Mathemaniac	原始链接
5 ways to derive the general term of Fibonacci sequence		Mathemaniac - Videos		Mathemaniac	原始链接
STAIRS reveal the relationship between Fibonacci and combinatorics	楼梯揭示斐波那契数列和组合学之间的关系。	Mathemaniac - Videos	Mathemaniac - 视频	Mathemaniac	原始链接
What do Fibonacci numbers have to do with combinatorics?		Mathemaniac - Videos		Mathemaniac	原始链接
Cosine law and properties of cyclic quadrilaterals	余弦定理和圆内接四边形的性质	Mathemaniac - Videos	Mathemaniac - 视频	Mathemaniac	原始链接
4 DIFFERENT ways to prove Heron's formula		Mathemaniac - Videos		Mathemaniac	原始链接
Generalizing methods to calculate square roots to cube roots		Mathemaniac - Videos		Mathemaniac	原始链接
EXPLAINED: Calculating square roots easily (BABYLONIAN and more)		Mathemaniac - Videos		Mathemaniac	原始链接
Calculating square roots easily IN 3 WAYS (BABYLONIAN and more)		Mathemaniac - Videos		Mathemaniac	原始链接
Math isn't ready to solve this problem		Aleph 0 - Videos		Aleph 0	原始链接
What is algebraic topology?		Aleph 0 - Videos		Aleph 0	原始链接
How to learn machine learning as a complete beginner: a self-study guide		Aleph 0 - Videos		Aleph 0	原始链接
The shocking connection between complex numbers and geometry.		Aleph 0 - Videos		Aleph 0	原始链接
What is a hole?		Aleph 0 - Videos		Aleph 0	原始链接
What is algebraic geometry?		Aleph 0 - Videos		Aleph 0	原始链接
The unsolvable problem that launched a revolution in set theory		Aleph 0 - Videos		Aleph 0	原始链接
The bridge between number theory and complex analysis		Aleph 0 - Videos		Aleph 0	原始链接
Algebraic number theory - an illustrated guide \| Is 5 a prime number?		Aleph 0 - Videos		Aleph 0	原始链接
How to self study pure math - a step-by-step guide		Aleph 0 - Videos		Aleph 0	原始链接
What is the square root of two? \| The Fundamental Theorem of Galois Theory		Aleph 0 - Videos		Aleph 0	原始链接
The Insolvability of the Quintic		Aleph 0 - Videos		Aleph 0	原始链接
The derivative isn't what you think it is.		Aleph 0 - Videos		Aleph 0	原始链接
Elliptic Curves and Modular Forms \| The Proof of Fermat’s Last Theorem		Aleph 0 - Videos		Aleph 0	原始链接
Poincare Conjecture and Ricci Flow \| A Million Dollar Problem in Topology		Aleph 0 - Videos		Aleph 0	原始链接
Navier Stokes Equation \| A Million-Dollar Question in Fluid Mechanics		Aleph 0 - Videos		Aleph 0	原始链接
Stokes' Theorem on Manifolds		Aleph 0 - Videos		Aleph 0	原始链接
Math News: The Triangle-to-Square problem has been solved!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
I got tenure!!! (here's how I did it)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How Google designed a smarter calculator than Apple		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
All the LOGARITHMS needed for calculus actually explained		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Kolmogorov Complexity		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My Self Study System		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
This integral is ridiculous.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Math News: Knights are 24/13 Times Faster Than Kings		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My favorite math fractals		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Math News: The Fish Bone Conjecture has been deboned!!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Solving 8 Differential Equations using 8 methods		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How I use AI in LaTeX -- my favorite workflow with Overleaf & Writefull		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Is Math Discovered or Invented?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What is 0^0? Is 0 a natural number? MATHEMATICIANS DISAGREE!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Can ChatGPT reason mathematically?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The longest mathematical proof ever		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Math News: The Bunkbed conjecture was just debunked!!!!!!!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Gaussian Algorithm Visualized		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
All the TRIG you need for calculus actually explained		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
This equation blew my mind // Euler Product Formula		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
ChatGPT is destroying my math exams		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Invariants: How Mathematicians Distinguish Between Objects		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
I'm leaving my professor job for YouTube		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The reason you should shuffle 7 times		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Could 1-1+1-1+1-1+1-1+... actually converge?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Why don't whales get more cancer? - Peto's Paradox		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to write your homework using LaTeX		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to fairly split weird bills using GAME THEORY		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Why hyperbolic functions are actually really nice		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Modelling with Differential Equations // Lanchester Square Collapse		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
5 counterexamples every calculus student should know		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My favorite way to compute Pi....experimentally!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Why complete chaos is impossible \|\| Ramsey Theory		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Math of Bubbles // Minimal Surfaces & the Calculus of Variations #SoME3		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Weird Topological Spaces // Connected vs Path Connected vs Simply Connected		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Solving the Gaussian Integral the cool way		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Why this pattern shows up everywhere in nature \|\| Voronoi Cell Pattern		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Dirichlet Integral is destroyed by Feynman's Trick		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Unlocking the secrets of Magic Square puzzles		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to write a STEM paper		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Fastest Multiplication Algorithm		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to make your LaTeX documents BEAUTIFUL // LaTeX Tutorial		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
YouTuber VS Professor		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Beauty of Symmetry: An Introduction to the Wallpaper Group		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Bernoulli Integral is ridiculous		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Gradient Descent \|\| Optimizing High-Dimensional Equations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My favorite LaTeX Tricks to save time		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The fastest matrix multiplication algorithm		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Fractal Snowflakes, Symmetries, and Beautiful Math Decorations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Topology is weird: The Ham Sandwich Theorem		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Tricky logarithmic differentiation example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Tables in LaTeX \|\| Full Tutorial \|\| Intro to LaTeX Episode 8		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Reciprocal Prime Series (this proof should be taught in calculus!)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The strangest function I know (linear but not continuous?? huh??)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Problem of Traffic: A Mathematical Modeling Journey		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How I Make Presentations Using LaTeX & Beamer		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
I almost failed calculus. Today I'm a math prof.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
This Infinitely Differentiable Function Breaks Taylor Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Your calculus prof lied to you (probably)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How I make beautiful GRAPHS and PLOTS using LaTeX		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Dirac's Belt Trick: Why a 2π rotation twists space but a 4π rotation fixes it		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Untangling the beautiful math of KNOTS		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Beyond the Binomial Theorem: The Binomial Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Beautiful Story of Non-Euclidean Geometry		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to make beautiful math graphics using Tikz & LaTeX		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Weird notions of "distance" \|\| Intro to Metric Spaces		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Variation of Parameters \|\| How to solve non-homogeneous ODEs		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Parseval's Identity, Fourier Series, and Solving this Classic Pi Formula		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
This Infinite Integral Tower Actually Converges? Sorta...		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
We need to talk about cheating in universities...		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What is cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos(…?? // Banach Fixed Point Theorem		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
CALCULUS SPEEDRUN \|\| Limits \|\| Episode 1		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Power Sets and the Cardinality of the Continuum		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My FINAL EXAM STUDY SYSTEM as a math prof	作为一名数学教授，我的期末考试复习系统	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
IS CHESS A GAME OF CHANCE? Classical vs Frequentist vs Bayesian Probability		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My favorite LaTeX packages for writing beautiful math documents	我最喜欢的用于编写精美数学文档的 LaTeX 宏包	Dr. Trefor Bazett - Videos	特雷福·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Bayesian Truth Serum // Using MATH to catch liars		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Stirling's Incredible Approximation // Gamma Functions, Gaussians, and Laplace's Method		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to write a thesis using LaTeX full tutorial		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Largest Numbers Ever Discovered // The Bizarre World of Googology		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The most important limit in Calculus // Geometric Proof & Applications		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Evolution of Cooperation // Iterated Prisoner's Dilemma		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Hierarchy of Big Functions \|\| n^n greater than n! greater than e^n greater than n^100		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to the Fundamental Group // Algebraic Topology with @TomRocksMaths		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Nash Equilibriums // How to use Game Theory to render your opponents indifferent		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My back to school routine as a PROFESSOR \| One week until classes start!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Mathematics of Trust // How Game Theory Explains Cooperation		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
MATH PROF vs TRICKY INTEGRALS		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to LaTeX Full Tutorial Part II (Equations, Tables, Figures, Theorems, Macros and more)	LaTeX 入门完整教程第二部分 (方程、表格、图、定理、宏等)	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
How to find DOMINATING STRATEGIES with Game Theory		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Normal Form Games // Intro to Game Theory // Episode 2		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to succeed as a math student // A conversation with Kyle Broder // Part I		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Formulas behind Savings, Investing, and Annuities	储蓄、投资和年金背后的公式	Dr. Trefor Bazett - Videos	博士特雷弗·巴泽特 - 视频	Dr. Trefor Bazett	原始链接
THE PRISONER'S DILEMMA // Intro to Game Theory // Episode 1		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Unboxing the world's most prestigious CHALK		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
INTEREST: Simple Interest vs Compound Interest vs Continuous Interest		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Learning CHESS vs Learning MATH	学习国际象棋对比学习数学	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
7 Ways to Level Up Your MATH SUPERPOWERS	提升你的数学超能力的7种方法	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
The beautiful geometric view of FOURIER SERIES // The Linear Algebra Perspective		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Computing the Fourier Series of EVEN or ODD Functions full example	计算偶函数或奇函数的傅立叶级数完整示例	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
How to Compute a FOURIER SERIES // Formulas & Full Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to FOURIER SERIES: The Big Idea		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Crazy Math Patterns that stop working......eventually		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Undetermined Coefficients: Solving non-homogeneous ODEs		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Mechanical Vibrations: Underdamped vs Overdamped vs Critically Damped		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Linear Programming	线性规划介绍	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
The Theory of Higher Order Differential Equations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Linear Independence of Functions & The Wronskian	函数的线性无关和朗斯基行列式	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Higher Order Constant Coefficient Differential Equations: y'''+y'=0 and y''''-3y'''+3y''-y'=0		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Constant Coefficient ODEs: Real & Distinct vs Real & Repeated vs Complex Pair		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to Solve Constant Coefficient Homogeneous Differential Equations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Theory of 2nd Order ODEs // Existence & Uniqueness, Superposition, & Linear Independence		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Logistic Growth Differential Equation	逻辑增长微分方程	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Autonomous Equations, Equilibrium Solutions, and Stability	自治方程、平衡解和稳定性	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
The Bernoulli Equation // Substitutions in Differential Equations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The worst ALGEBRA MISTAKES I see as a Math Prof don't do these		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Method of Integrating Factors for Linear 1st Order ODEs full example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Linear Differential Equations & the Method of Integrating Factors		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Big Theorem of Differential Equations: Existence & Uniqueness		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Great Gatsby Curve: Income Immobility vs Income Inequality		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Geometric Meaning of Differential Equations // Slope Fields, Integral Curves & Isoclines		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Newton's Law of Cooling // Separable ODE Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Separation of Variables // Differential Equations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Key Definitions of Differential Equations: ODE, order, solution, initial condition, IVP		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What is a DIFFERENTIAL EQUATION?? Intro to my full ODE course		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My STUDY ROUTINE as a Math Prof // My top study tips		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)	向量微积分的统一视角 (斯托克斯定理, 散度定理 & 格林定理)	Dr. Trefor Bazett - Videos	特里福尔·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus	从矢量微积分的散度定理推导高斯电通量定律	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Divergence Theorem for regions bounded by two surfaces // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Divergence Theorem example: Flux across unit cube // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Stokes' Theorem Example // Verifying both Sides // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Stokes' Theorem // Geometric Intuition & Statement // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The CURL of a 3D vector field // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Computing the Flux Across a Surface // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Flux of a Vector Field Across a Surface // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Orientable vs Non-Orientable Surfaces and the Mobius Strip		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Surface Integrals // Formulas & Applications // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Computing the Surface Area of an Implicitly Defined Surface		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Surface Area for Implicit & Explicit Surfaces // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Computing the Surface Area of a surface parametrically // Example 2 // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Computing the Surface Area of a surface parametrically // Example 1 // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What is VECTOR CALCULUS?? Full Course Introduction		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Why is the surface area of a Sphere 4pi times radius squared???		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Surface Area formula for Parametric Surfaces // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Example: Using Green's Theorem to Compute Circulation & Flux // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Divergence, Flux, and Green's Theorem // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Finding the scalar potential function for a conservative vector field // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Math Prof answers 6÷2(1+2) = ? once and for all *Viral Math Problem*		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Curl, Circulation, and Green's Theorem // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Curl or Circulation Density of a Vector Field // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to Test if a Vector Field is Conservative // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Conservative Vector Fields // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Curves, Parameterizations, and the Arclength Parameterization	曲线、参数化和弧长参数化	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Flux Integrals // Big Idea, Formula & Examples // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Flow Integrals and Circulation // Big Idea, Formula & Examples // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Line Integrals with respect to x or y // Vector Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Example: Computing the Line Integral of a Vector Field (i.e. Work Done)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Line Integrals of Vector Fields // Big Idea, Definition & Formula		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Gradient Vector Field	梯度向量场	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Intro to VECTOR FIELDS // Sketching by hand & with computers		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Line Integrals in 3D // Formula & Three Applications		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Line Integrals: Full Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What is a LINE INTEGRAL? // Big Idea, Derivation & Formula		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Markov Chains & Transition Matrices	马尔可夫链与转移矩阵	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Intro to Markov Chains & Transition Diagrams	马尔可夫链与转移图入门	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
The largest Mersenne prime is 2^82589933-1....so far	最大的梅森素数是 2 的 82589933 次方减 1，到目前为止。	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Defining Numbers & Functions Using SET THEORY // Foundations of Mathematics		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Polar Form of COMPLEX NUMBERS // Finding the nth roots of -1		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The geometric view of COMPLEX NUMBERS		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 1		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Gaussian Integral // Solved Using Polar Coordinates		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Change the order of integration to solve tricky integrals	改变积分顺序来解决棘手的积分	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Counting with Triple Intersections // Example & Formula		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Vector Space of Polynomials: Span, Linear Independence, and Basis		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How SIMPSON'S PARADOX explains weird COVID19 statistics		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
9 tips to help you PROVE MATH THEOREMS		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The bizarre world of INFINITE rearrangements // Riemann Series Theorem		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Lagrange Multipliers with TWO constraints \| Multivariable Optimization		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Multivariable Optimization with Boundaries	带边界约束的多变量优化	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Geometric Meaning of the Gradient Vector	梯度向量的几何意义	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
What is differentiability for multivariable functions??		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Continuity vs Partial Derivatives vs Differentiability \| My Favorite Multivariable Function		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Computing Multivariable Limits Algebraically		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How I make EDUCATION VIDEOS		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to use SERIES to solve DIFFERENTIAL EQUATIONS example: Airy's Equation y''-xy=0		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
When can you use Series to solve ODEs? Ordinary vs Singular Points		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to solve ODEs with infinite series \| Intro & Easiest Example: y'=y		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
False Positives & Negatives for COVID-19 tests \| Using Bayes' Theorem to Estimate Probabilities		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Tangential and Normal components of Acceleration \| Multi-variable Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Solving ODEs with Delta functions using Laplace Transforms		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Dirac Delta 'Function': How to model an impulse or infinite spike		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to LaTeX : Learn to write beautiful math equations \|\| Part 1		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Periodic Functions and the Laplace Transform	周期函数和拉普拉斯变换	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
What are the big ideas of Multivariable Calculus?? Full Course Intro		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Laplace Transform and Piecewise or Discontinuous Functions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Derivatives & Integrals of Laplace Transforms \| Ex: Bessel Equation ty''+y'+ty=0		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Defining the Natural Logarithm as an Integral?!?!?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Why Exponential Growth?? Intro to Separable Differential Equations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Convolution of Two Functions \| Definition & Properties		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to use Laplace Transform to solve Differential Equations Full Example	如何使用拉普拉斯变换求解微分方程完整示例	Dr. Trefor Bazett - Videos	博士 Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Inverse Laplace Transform Example using Partial Fractions	使用部分分式法的拉普拉斯逆变换示例	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
The MATH of Epidemics \| Variants of the SIR Model		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Translation and Inverse Laplace Transforms	平移和拉普拉斯逆变换	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Using Laplace Transforms to solve Differential Equations *full example*		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Laplace Transform of Derivatives and Integrals		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
3 Properties of Laplace Transforms: Linearity, Existence, and Inverses		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to the Laplace Transform & Three Examples	拉普拉斯变换入门与三个例子	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 – 视频	Dr. Trefor Bazett	原始链接
The MATH of Pandemics \| Intro to the SIR Model		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
COMPLEX Eigenvalues, Eigenvectors & Diagonalization full example	复数特征值、特征向量与对角化完整示例	Dr. Trefor Bazett - Videos	Trefor Bazett博士 - 视频	Dr. Trefor Bazett	原始链接
Intro to Dimensional Analysis: How Much Energy in an Atomic Bomb? Or a Supernova?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to LEARN effectively \| Five evidence-based tips		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Change of Variables & The Jacobian \| Multi-variable Integration		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Integration in Spherical Coordinates	球坐标中的积分	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Triple Integrals in Cartesian Coordinates \| Volume between Surfaces		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Double Integration in Polar Coordinates \| Example & Derivation		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Double Integration Example over General Regions --- two ways!	一般区域上的二重积分示例 --- 两种方法！	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Defining Double Integration with Riemann Sums \| Volume under a Surface		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Lagrange Multipliers \| Geometric Meaning & Full Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Multi-variable Optimization & the Second Derivative Test	多变量优化与二阶导数判别法	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
How to find the TANGENT PLANE \| Linear approximation of multi-variable functions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Directional Derivatives \| What's the slope in any direction?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Multi-Variable Chain Rule: Derivatives of Compositions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What are derivatives in 3D? Intro to Partial Derivatives		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Limits are...weird...for multi-variable functions \| Limits along paths		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Visualizing Multi-variable Functions with Contour Plots		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Torsion: How curves twist in space, and the TNB or Frenet Frame		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How curvy is a curve? Intro to Curvature & Circles of Curvature \| Multi-variable Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How long is a curve?? The Arclength Formula in 3D		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
3D Curves and their Tangents \| Intro to Vector-Valued Functions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Equations of Planes: Vector & Component Forms \| Multivariable Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Vector Equation of Lines \| Multivariable Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Geometrically Defining the Cross Product \| Multivariable Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Angle between vectors leads to defining the Dot Product \| Multivariable Calculus		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
New Job. New Country. New Math Videos.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Why is the area of a circle equal to π r² ??? 2000 year old proof, but with pizza.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Conditional Probability With Tables \| Chance of an Orange M&M???		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Sketching Polar Curves		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Polar Coordinates		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Arclength of Parametric Curves		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Area under a Parametric Curve \| Formula, Derivation, & Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Tangents to Parametric Curves \| Multiple tangents at the same point!!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Estimating the Remainder of a Series Approximation via the Integral Test	利用积分判别法估计级数近似的余项	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Plotting Parametric Curves		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Why Taylor Series actually work: The Taylor Inequality		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
3 Applications of Taylor Series: Integrals, Limits, & Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Taylor Series: Approximations on Steroids		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Power Series & Intervals of Convergence	幂级数与收敛区间	Dr. Trefor Bazett - Videos	博士 Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Solving Inequalities with Absolute Values: Ex \|x-2\| less than 3		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Choosing Which Convergence Test to Apply to 8 Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Ratio & Root Tests \| Geometric Series Generalized		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Absolute Convergence vs Conditional Convergence vs Convergence	绝对收敛对条件收敛对收敛	Dr. Trefor Bazett - Videos	博士特里弗·巴泽特 - 视频	Dr. Trefor Bazett	原始链接
Alternating Series \| Estimating the Remainder		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Alternating Series Test \| Intuition, Statement & Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Limit Comparison Test for Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Comparison Test for Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Integral Test \| Derivation & 1st Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Harmonic Series \| It diverges, but insanely slowly!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Geometric Series \| Convergence, Derivation, and Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Series: What is 1/2+1/4+1/8+1/16+...?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Limits of Sequences, Limit laws & Function Representations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Sequences	序列入门	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Infinite Surface Area but Finite Volume!?!? Gabriel's Horn		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Area of Surfaces of Revolution \| Derivation & Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Arclength Formula \| Derivation & Ex: Circumference of a Circle		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Comparison Test for Improper Integrals	广义积分的比较判别法	Dr. Trefor Bazett - Videos	特里福·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Improper Integrals: How to Integrate with Infinities, 2 ways!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Partial Fractions \| Repeating and irreducible Quadratic Terms		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
3 Ways to Show a Logical Equivalence \| Ex: DeMorgan's Laws		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Integration by Partial Fractions \| Big Idea + First Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Deconstructing a messy integral \| Trig subs & u-subs combined		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Trig Subs \| How To Choose The Substitution & Deal With Indefinite Integrals		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Trigonometric Substitution --- Ex: Deriving Area of Circle Formula		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Trigonometric Integrals --- ∫sin^n(x)cos^m(x)dx via Pythagorean or Half-Angle Identities		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Two Tricky Integration By Parts Examples	两个棘手的分布积分例子	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Intro to Integration By Parts --- Examples: ∫xsinxdx & ∫arctan(x)dx		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
My Favorite Theorem: The Borsuk-Ulam Theorem		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Euler Paths & the 7 Bridges of Konigsberg \| Graph Theory		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Degree of Vertices \| Definition, Theorem & Example \| Graph Theory		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Properties in Graph Theory: Complete, Connected, Subgraph, Induced Subgraph		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Graph Theory \| Definitions & Ex: 7 Bridges of Konigsberg		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Average Value of a Continuous Function on an Interval		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Exam Walkthrough \| Calc 1, Test 3 \| Integration, FTC I/II, Optimization, u-subs, Graphing		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Fundamental Theorem of Calculus II		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Fundamental Theorem of Calculus 1 \| Geometric Idea + Chain Rule Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Folding a wire into the largest rectangle \| Optimization example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Ex: Optimizing the Volume of a Box With Fixed Surface Area		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Rational Numbers \| Definition + First Proof		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to Prove Math Theorems \| 1st Ex: Even + Odd = Odd		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Formal Definitions in Math \| Ex: Even & Odd Integers		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Infinite Limit vs Limits at Infinity of a Composite Function		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Example: When is a Piecewise Function Continuous?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Definition of Derivative Example: f(x) = x + 1/(x+1)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to Succeed in Online Courses		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to Find the Equation of a Tangent Line	如何求切线的方程	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
The Empty Set & Vacuous Truth	空集与空真	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Top 4 Algebraic Tricks for Computing Limits	计算极限的四大代数技巧	Dr. Trefor Bazett - Videos	博士特雷弗·巴泽特 - 视频	Dr. Trefor Bazett	原始链接
How to use Spaced Retrieval to memorize facts....forever!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Visualizing Diagonalization & Eigenbases		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Visualizing Change Of Basis Dynamically		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Changing Between Two Bases \| Derivation + Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Dimension Theorem \| Dim(Null(A)) + Dim(Col(A)) = n \| Also, Rank!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Coordinate Systems From Non-Standard Bases \| Definitions + Visualization		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Writing Vectors in a New Coordinate System Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Computing Dimension of Null Space & Column Space		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Dimension of a Subspace \| Definition + First Examples		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What Exactly are Grid Lines in Coordinate Systems?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Making a Math Concept Map \| Ex: Linear Independence		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Vector Spaces \| Definition & Examples		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Null Space & Column Space of a Matrix \| Algebraically & Geometrically		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Span is a Subspace \| Proof + Visualization		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Subspaces are the Natural Subsets of Linear Algebra \| Definition + First Examples		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Invertible Matrices correspond with Invertible Transformations proof	可逆矩阵对应可逆变换证明	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Visualizing Invertible Transformations (plus why we need one-to-one)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Visualizing Composition of Linear Transformations aka Matrix Multiplication	可视化线性变换的复合（也称作矩阵乘法）	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
5 Tips To Make Math Practice Problems Actually Effective	5个让数学练习题真正有效的技巧	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Proving Algebraic Rules in Linear Algebra --- Ex: A(b+c) = Ab +Ac		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Introducing Linear Combinations & Span		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What is a vector? Visualizing Vector Addition & Scalar Multiplication		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Visualizing Solutions to Linear Systems - - 2D & 3D Cases Geometrically	线性方程组解的几何可视化 -- 二维和三维情况	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
What is a Solution to a Linear System? Intro		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Cantor's Diagonal Argument: The rationals and reals have different sizes?!?!?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Integers & Rationals are both infinite but is it the SAME infinity?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
New Math Studio + Channel Update		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
A beautiful combinatorical proof of the Brouwer Fixed Point Theorem - Via Sperner's Lemma	布劳威尔不动点定理的一个优美的组合证明——通过斯佩纳引理	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
What's the big idea of Linear Algebra? Course Intro		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Bayes' Theorem Example: Surprising False Positives	贝叶斯定理示例：令人惊讶的假阳性	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Welcome to Calculus II	欢迎来到微积分 II	Dr. Trefor Bazett - Videos	崔福·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
The End of Discrete Math - Congrats! Some final thoughts...		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
♥♥♥ Thank you Calc Students♥♥♥ Some final thoughts.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Bayes' Theorem - Example: A disjoint union		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Bayes' Theorem - The Simplest Case		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Two Conditional Probability Examples (what's the difference???)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Conditional Probability	条件概率入门	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Counting and Probability Walkthrough	计数和概率演练	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Optimization Example: Minimizing Surface Area Given a Fixed Volume		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
"Reverse" Riemann Sums \| Finding the Definite Integral Given a Sum		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Back Substitution - When a u-sub doesn't match cleanly!	回代 - 当 u代换无法完美匹配时!	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Induction Proofs Involving Inequalities.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
You need to check EVERY spot for reflexivity, symmetry, and transitivity		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Substitution Method for Definite Integrals careful!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Adjusting the Constant in Integration by Substitution		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Substitution - Undoing the Chain Rule	换元法入门 - 链式法则的逆运算	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Using the Element Method to prove a Set Containment w/ Modus Tollens		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Tips for Success in Flipped Classrooms + OMG BABY!!!	翻转课堂的成功秘诀 + OMG 宝贝!!!	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
The Definite Integral Part III: Evaluating From The Definition		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Definite Integral Part II: Using Summation Notation to Define the Definite Integral		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Definite Integral Part I: Approximating Areas with rectangles		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Solving for the constant in the general anti-derivative		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What's an anti-derivative?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Applying L'Hopital's Rule to Exponential Indeterminate Forms	将洛必达法则应用于指数不定式	Dr. Trefor Bazett - Videos	特雷福·贝泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Using L'Hopital's Rule to show that exponentials dominate polynomials	使用洛必达法则证明指数函数支配多项式	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Relative and Absolute Maximums and Minimums \| Part II		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The MEAN Value Theorem is Actually Very Nice		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Relative and Absolute Maximums and Minimums \| Part I		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Related Rates	相关变化率入门	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Linear Approximations \| Using Tangent Lines to Approximate Functions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Logarithmic Differentiation \| Example: x^sinx		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Derivative of ln(x) via Implicit Differentiation		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Derivative of Inverse Trig Functions via Implicit Differentiation		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Implicit Differentiation \| Differentiation when you only have an equation, not an explicit function		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Negating Logical Statements with Multiple Quantifiers		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Universal Conditionals P(x) implies Q(x)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
A Limit Example Combining Multiple Algebraic Tricks		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Chain Rule using Leibniz notation		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Chain Rule: the Derivative of a Composition		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Interpreting the Chain Rule Graphically	图解解释链式法则	Dr. Trefor Bazett - Videos	Trefor Bazett博士 - 视频	Dr. Trefor Bazett	原始链接
The derivative of Trigonometric Functions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The product and quotient rules	乘法法则和除法法则	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
The derivative of e^x.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Derivative Rules: Power Rule, Additivity, and Scalar Multiplication		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The derivative of a constant and of x^2 from the definition	根据定义，常数和 x^2 的导数	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Computing Limits at Infinity for Rational Functions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Discrete Math - Welcome to the Course!	离散数学导论 - 欢迎来到本课程！	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Applying the Definition of the Derivative to 1/x		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Limits "at" infinity	无穷远处的极限	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Were you ever exactly 3 feet tall? The Intermediate Value Theorem		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Definition of the Derivative \| Part I		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Limits are simple for continuous functions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Limits of Oscillating Functions and the Squeeze Theorem	振荡函数的极限和夹逼定理	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Building up to computing limits of rational functions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Limit Laws \| Breaking Up Complicated Limits Into Simpler Ones		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What is an infinite limit?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
A Tale of Three Functions \| Intro to Limits Part II		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
A Tale of Three Functions \| Intro to Limits Part I		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Velocity Problem \| Part II: Graphically		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Velocity Problem \| Part I: Numerically		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Reducing the Least Squares Approximation to solving a system		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Least Squares Approximations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Full example: using Gram-Schmidt		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Using Gram-Schmidt to orthogonalize a basis	使用施密特正交化法正交化一组基	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
How many ways are there to reorder the word MISSISSIPPI? // Choose Formula Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Combinations Formula: Counting the number of ways to choose r items from n items.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Counting formula for two intersecting sets: N(A union B)=N(A)+N(B)-N(A intersect B)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The summation rule for disjoint unions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The geometric view on orthogonal projections		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Proving that orthogonal projections are a form of minimization	证明正交投影是一种最小化	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Orthogonal Decomposition Theorem Part II	正交分解定理第二部分	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Orthogonal Decomposition Theorem Part 1: Defining the Orthogonal Complement		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Orthogonal bases are easy to work with!	正交基底易于处理！	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Permutations: How many ways to rearrange the letters in a word?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
What is the probability of guessing a 4 digit pin code?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Example: Computing Probabilities using P(E)=N(E)/N(S)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Introduction to probability // Events, Sample Space, Formula, Independence		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Distance, Angles, Orthogonality and Pythagoras for vectors		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Dot Products and Length	点积和长度	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
The Similarity Relationship Represents a Change of Basis		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Equivalence Relations - Reflexive, Symmetric, and Transitive	等价关系 - 自反性、对称性、传递性	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Reflexive, Symmetric, and Transitive Relations on a Set	集合上的自反、对称和传递关系	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Relations and their Inverses		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Full Example: Diagonalizing a Matrix		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Compute large powers of a matrix via diagonalization		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How the Diagonalization Process Works	对角化过程是如何工作的	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Diagonal Matrices are Freaking Awesome	对角矩阵真是太棒了	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Proving equalities of sets using the element method		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Universes and Complements in Set Theory	集合论中的全集和补集	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
The Intersection of Two Sets	两个集合的交集	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
The union of two sets		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Prove A is a subset of B with the ELEMENT METHOD		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Similar matrices have similar properties		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
A range of possibilities for eigenvalues and eigenvectors	特征值和特征向量的各种可能性	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
The Miraculous Fibonacci Sequence	神奇的斐波那契数列	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Recursive Sequences		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Example: Computing Eigenvalues and Eigenvectors		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Using determinants to compute eigenvalues & eigenvectors	使用行列式计算特征值和特征向量	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
What eigenvalues and eigenvectors mean geometrically	特征值和特征向量的几何意义	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Finding a basis for Col(A) when A is not in REF form.	找到 A 的列空间的一个基，当 A 不是行阶梯形式时。	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Example: Writing a vector in a new basis		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Visualizing a vector in multiple coordinate systems	在多个坐标系中可视化向量	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Deriving the Change-of-Basis formula		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Rank, and the Relationship between Col(A) and Null(A)		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Strong Induction // Intro and Full Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The sum and product of finite sequences	有限序列的和与积	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Finding the Dimension of a Subspace		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Gridlines in nonstandard coordinate systems.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Mathematical Induction		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Writing Vectors in Different Coordinate Systems		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Finding a Basis for the Nullspace or Column space of a matrix A	求解矩阵 A 的零空间或列空间的一组基	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
The Basis of a Subspace	子空间的基	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
The formal definition of a sequence.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Introduction to sequences	数列概论	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Proof: There are infinitely many primes numbers		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Proof by Contrapositive \| Method & First Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Proof by Contradiction \| Method & First Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Null Space and Column Space of a Matrix		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Subspaces of R^n		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Determinants can be computed along any row or column - choose the easiest!	行列式可以沿任意行或列计算 - 选择最简单的！	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Determinants - a "quick" computation to tell if a matrix is invertible		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Proof by Division Into Cases		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Quotient-Remainder Theorem and Modular Arithmetic		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Disproving implications with Counterexamples	使用反例证明蕴涵不成立	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Invertible Transformations	可逆变换	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
How does 1:1 and onto relate to invertibility?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
When does a matrix fail to be invertible? Also more "Big Theorem".		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Proving that divisibility is transitive		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to watch math videos		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Find the Inverse of a Matrix		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Finding inverses to 2x2 matrices is easy!	求 2x2 矩阵的逆矩阵很简单！	Dr. Trefor Bazett - Videos	博士特雷弗·巴泽特 - 视频	Dr. Trefor Bazett	原始链接
You can "invert" matrices to solve equations...sometimes!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Elementary Matrices		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Negating Universal and Existential Quantifiers	否定全称量词和存在量词	Dr. Trefor Bazett - Videos	博士特里弗·巴泽特 - 视频	Dr. Trefor Bazett	原始链接
Step-By-Step Guide to Proofs \| Ex: product of two evens is even		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Universal and Existential Quantifiers, ∀ "For All" and ∃ "There Exists"		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Predicates and their Truth Sets		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Necessary and Sufficient Conditions	必要条件和充分条件	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Computing matrix multiplication	计算矩阵乘法	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
The motivation and definition of Matrix Multiplication		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Algebraic operations on Matrices - scalar multiplication, matrix addition, and transposition		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
One-to-one, Onto, and the Big Theorem Part II	单射、满射和大数据理第二部分	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士视频	Dr. Trefor Bazett	原始链接
Finding the Matrix of a Linear Transformation		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Matrix Transformations are the same thing as Linear Transformations	矩阵变换就是线性变换。	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Every vector is a linear combination of the same n simple vectors!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Analyzing an argument for validity		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Logical Argument Forms: Generalizations, Specialization, Contradiction		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Logical Arguments - Modus Ponens & Modus Tollens		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Transformations and Matrix Transformations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Are Matrix Transformations and Linear Transformation the same? Part I		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Linear Transformations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Three examples of Matrix Transformations	矩阵变换的三个例子	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Determining Linear Independence vs Linear Dependence	线性独立性与线性相关性的判定	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Linear Dependence and Independence - Geometrically	线性相关与独立 - 从几何角度	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Top eight professions.....do they require math skills???		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Three nice properties of homogeneous systems of linear equations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Geometric View on Solutions to Ax=b and Ax=0.		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Writing solutions to Ax=b in vector form	将 Ax=b 的解写成向量形式	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Biconditional Statements \| "if and only if"		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The converse and inverse of a conditional statement	条件语句的逆命题和否命题	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Contrapositive of a Conditional Statement	条件语句的逆否命题	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Negating a Conditional Statement		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Vacuously True Statements		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Conditional Statements: if p then q		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Tautologies and Contradictions	重言式与矛盾式	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Logical Equivalence of Two Statements	两个命题的逻辑等价	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Truth Table Example: ~p V ~q		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Truth Tables \| Negation, Conjunction, and Disjunction		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intro to Logical Statements	逻辑语句导论	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
The Big Theorem, Part I		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Matrix-Vector Multiplication Example	矩阵-向量乘法示例	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Matrix-Vector Multiplication and the equation Ax=b	矩阵向量乘法和方程 Ax=b	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
How to determine if one vector is in the span of other vectors?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Linear Combinations and Span -- Part II		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Linear Combinations and Span -- Part I		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Vectors, both Algebraically and Geometrically		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Example: Is this relation a function?		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Formal Definition of a Function using the Cartesian Product	使用笛卡尔积的函数的形式定义	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
The intuitive idea of a function		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Back Substitution with infinitely many solutions	带有无穷多解的回代	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Row Echelon Form and Reduced Row Echelon Form	行阶梯形和简化行阶梯形	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Examples with 0, 1, and infinitely many solutions to linear systems	关于线性系统0解、唯一解和无穷多解的例子	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Using Elementary Row Operations to simplify a linear system	使用初等行变换简化线性系统	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Using Elementary Row Operations to Solve Systems of Linear Equations	使用初等行变换求解线性方程组	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Rewriting a Linear System using Matrix Notation	用矩阵记法重写线性系统	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Relations between two sets \| Definition + First Examples		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Cartesian Product of Two Sets A x B	两个集合 A 和 B 的笛卡尔积	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Welcome to Linear Algebra		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Set-Roster vs Set-Builder notation	列表法与构造法	Dr. Trefor Bazett - Videos	特雷弗巴泽特博士视频	Dr. Trefor Bazett	原始链接
Intro to Sets \| Examples, Notation & Properties		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Geometric meaning of a linear system in 2D	二维线性系统的几何意义	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Geometric meaning of solutions to a linear equation in 2D	二维线性方程解的几何意义	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Systems of Linear Equations		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Intersections of Planes		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Example: Finding the equation of a weird plane		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Equation of a plane	平面的方程	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Lines Three Ways		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Geometric Interpretation of Cross Product and Triple Product		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
The Cross Product		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Introduction to Vectors	向量引论	Dr. Trefor Bazett - Videos	博士特雷弗·巴泽特—视频	Dr. Trefor Bazett	原始链接
Equations in 3 Dimensions		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Areas in Polar Coordinates	极坐标中的面积	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Example: Area Inside Polar Curves		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Curve Sketching in Polar Coordinates		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Tangents to Polar Curves	极坐标曲线的切线	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Polar Coordinates		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Arclength of curves given parametrically		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Area under a curve given parametrically		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Tangents to Parametric Curves	参数曲线的切线	Dr. Trefor Bazett - Videos	博士特雷弗·巴泽特 - 视频	Dr. Trefor Bazett	原始链接
Parametric Curves		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Getting new Taylor series from old ones	从旧的泰勒级数得到新的	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Tayor Series Part 2		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Taylor Series Part I		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Power Series \| Determining endpoints of the interval of convergence		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Introduction to Power Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Root Test	根号判别法	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Ratio Test	比值判别法	Dr. Trefor Bazett - Videos	Dr. Trefor Bazett - 视频	Dr. Trefor Bazett	原始链接
Absolute and Conditional Convergence		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Alternating Series \| Estimating Remainers		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Alternating Series \| Definition and Convergence		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Limit Comparison Test for Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Comparison Test for Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Integral Test for Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Using the Integral Test to Estimate Remainders of Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Integral Test - Bonus Example	积分判别法 - 附加例子	Dr. Trefor Bazett - Videos	特里弗·巴泽特博士—视频	Dr. Trefor Bazett	原始链接
Integral Test for Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Telescoping Series	裂项级数	Dr. Trefor Bazett - Videos	博士特雷弗·巴泽特：视频	Dr. Trefor Bazett	原始链接
Algebraic Laws for Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Divergence Test for Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Introduction to Series \| Definition, Convergence, and Geometric Series		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Bounded and Monotonic Sequences		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Introduction to Sequences Part II: Computing limits		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Introduction to Sequences Part I: Definition, Examples, and Convergence		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Trigonometric Substitution		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Trigonometric Integrals	三角函数积分	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Partial Fractions Part 1		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
How to watch these videos		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Integration by Parts	分部积分	Dr. Trefor Bazett - Videos	特里弗·巴泽特 - 视频	Dr. Trefor Bazett	原始链接
Trig Substitutions Part 2		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Improper Integrals Part II		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Comparison Test for Integrals	积分比较判别法	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Improper Integrals Part I	广义积分第一部分	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Partial Fractions Part II	部分分式第二部分	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Surface Area Part I: Revolving around the x-axis		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Surface Area Part II: Revolving around the y-axis		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Arclength - Definition and Example		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Choosing what integration methods to use - Challenging Example!		Dr. Trefor Bazett - Videos		Dr. Trefor Bazett	原始链接
Choosing what integration methods to use - Part I	集成方法的选择 - 第一部分	Dr. Trefor Bazett - Videos	Trefor Bazett 博士 - 视频	Dr. Trefor Bazett	原始链接
Multiplication of Complex Numbers in Polar Form	极坐标形式复数的乘法	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The SEVENTH of the seven beauties: the derivation of the integral of signed curvature		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The SEVENTH of the seven beauties: The integral of signed curvature over a closed curve		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Polar Form of Complex Numbers		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
De Moivre's Formula for Complex Numbers: A Precursor to Euler's Formula		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Elementary Properties of Complex Numbers According to Hamilton		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Accepting Complex Numbers: Hamilton vs Euler		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Birth of Complex Numbers and Tartaglia's Formula	复数的诞生和塔尔塔利亚公式	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Tartaglia's Formula in Action and Numbers of the form a+b√5	塔尔塔利亚公式的应用与形如 a+b√5 的数	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tartaglia's Formula in Action: Two Examples		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Euler's Derivation of the Tartaglia-Cardano Formula		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Polynomial Equations and the Fundamental Theorem of Algebra	多项式方程与代数基本定理	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The SIXTH of the seven beauties. The integral of position vector dotted with unit normal.	七大美学中的第六个。位置向量点乘单位法向量的积分。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The FIFTH of the seven beauties. The integral of position vector dotted with unit tangent.		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The FOURTH of the seven beauties. The integral of position vector dotted curvature normal.		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The THIRD of the seven beauties. The integral of unit normal over a curve.	七大美事之第三。单位法向量沿曲线的积分。	MathTheBeautiful - Videos	美丽数学 - 视频	MathTheBeautiful	原始链接
The SECOND of the seven beauties! The integral of curvature normal over a curve.	七大美妙的第二项！沿曲线对曲率法向量的积分。	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
A brief review of curves and integration over curves.		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The FIRST of the seven beauties! The integral of unit tangent over a curve.	七大美景之首！曲线上的单位切向量积分。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Expression for the Arc Length of a Curve in Cartesian Coordinates	在笛卡尔坐标系中曲线的弧长表达式	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
The Geometric Expression for the Arc Length of a Curve	曲线弧长的几何表达式	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
From Physical to Arithmetic Integrals - Achieving Complete Agreement with Intuition	从物理积分到算术积分 - 实现与直觉的完全一致	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Hate most advanced math books? These words of encouragement are for you		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
From Physical to Arithmetic Integrals - How to Achieve Invariance	从物理积分到算术积分 - 如何实现不变性	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Converting a Physical Integral into an Arithmetic One: Identifying the Challenge		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Why Change of Variables Is Often an Inherently Ambiguous Task	为什么变量替换往往是一项本质上模糊的任务	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Derivative of the Inverse Function, or How to Reparameterize a Curve		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Derivative of the Inverse Function - Why It Is Confusing (and how to eventually fix it)	反函数的导数 - 为什么它令人困惑 (以及最终如何解决它)	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Integration by Substitution Is an Application of the Chain Rule	换元积分是链式法则的应用。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Need for Arbitrary Parameterizations of Curves		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Arithmetic Integrals And the Fundamental Theorem of Calculus		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Geometric Integrals - a Fundamental Concept to Be Accepted on an Intuitive Basis	几何积分 - 一个应凭直觉领会的基本概念	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Hypersurfaces, Unit Normals, and Signed Curvature	超曲面、单位法向量和带符号曲率	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
The Curvature of a Curve, Its Principal Normal, And Its Osculating Plane	曲线的曲率、主法线和密切平面	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Torsion of a Curve		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Decomposition by the Dot Product	点积线性分解	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
The Arc Length Parameterization	弧长参数化	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Analysis of the Unit Circle as a Planar Curve in Differential Geometry.	微分几何中单位圆作为平面曲线的分析	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Closest Point on a Curve to a Given Point: Combing Calculus And Geometry		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Kinematic Analysis of a Rigid Bar		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Classical Euclidean Geometry Is Limited to Three Dimensions	经典欧几里得几何局限于三维。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Constant Speed Motion - Analysis via differentiation of vector-valued functions	匀速运动 - 通过向量值函数的微分进行的分析	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Properties of Vector Differentiation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Main Intuitive Idea of Calculus (applied to curves in Differential Geometry)	微积分的主要直观思想 (应用于微分几何中的曲线)	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
The Geometric Interpretation of the DERIVATIVE of a Vector-Valued Function		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Geometric Interpretation of a Vector-Valued Function: It's a curve - end of story.		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Differentiation of Vectors: What It Actually Means to DIfferentiate a Vector-Valued Function!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
My Proof of Pythagoras' Theorem is NOT circular!	我的勾股定理证明不是循环的！	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
The Heights of a Triangle Are Concurrent, a Vector-Based Proof That Does Not Require Any Ingenuity!	三角形的高共点，一个无需任何技巧的基于向量的证明！	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Orthogonal Projection Expressed in Terms of The Dot Product	正交投影用点积表示	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Ceva's Theorem, A Vector Based Proof - No Ingenuity Required! Concurrent Lines in a Triangle	塞瓦定理，一个基于向量的证明 - 无需技巧！三角形中的共点线。	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
The Bisector Theorem: A Vector-Based Proof - No Ingenuity Required!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Medians of a Triangle Are Concurrent, A Vector-Based Proof - As Straightforward as It Gets!	三角形的中线是共点的，一个基于向量的证明——再简单不过了！	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Introduction to Affine Spaces: What you can do in Linear Algebra w/o inner products. Less Is More!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A Simple Solution to an Otherwise Challenging Problem - Algebra and Geometry Working Together!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Vector Equation of a Straight Line. This will help us solve a number of difficult problems soon!	直线的向量方程。这很快将帮助我们解决许多难题！	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Diagonals of a Rhombus Intersect at a Right Angle - A Dot Product Proof	菱形的对角线垂直相交 — 点积证明	MathTheBeautiful - Videos	美丽数学 - 视频	MathTheBeautiful	原始链接
The Dot Product Proof of the Pythagorean Theorem - The power of Vectors Is on Full Display!	向量点积证明勾股定理 - 向量的威力尽显！	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Dot Product and the Inner Product: Comparing These Key Concepts in Linear Algebra, Geometry, ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
What Is a Vector? It depends! Geometric perspective vs Linear Algebra vs ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Mr. Tibbs, the Queen's butler in BFG made a math mistake. Did the Movie Get It Right? We Investigate		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Squaring the Parabola by Means of Ordinary Calculus: A lesson in containing analytical calculations		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A Lesson in Daring, Flair, and Beauty: Archimedes' Incredible Breakthrough in Squaring the Parabola		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
How Archimedes "Squared" the Sphere or One of the Greatest Unifying Moments in Science History		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Challenge of π or How Archimedes Squared the Circle. Introduction to Differential Geometry	π的挑战或阿基米德如何化圆为方。微分几何导论。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Why Does Area Change Quadratically w/ Size? A Simple Question That Requires the Concept of Infinity		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
How the Greeks Approached the Concept of Area. Archimedes' Method of Exhaustions	希腊人如何看待面积的概念。阿基米德的穷竭法。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Areas and the trouble with √2. Lesson 2 of a complete course on Differential Geometry		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The MOST Fundamental Concepts in Differential Geometry, & SURPRISE: Math always start in the middle!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Gilbert Strang's Final MIT Lecture		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Strang Decomposition A = CR	斯特朗分解 A = CR	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
The connection between the cross product and the determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
An elementary surface integral formula you've never heard of		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 25: The Frenet Identities for a Planar Curve		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 24: The Principal Normal and Curvature of a Planar Curve		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 23: The Laws of Vector Differentiation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 22: The Distance Between a Point and a Curve		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 20: Heron's Problem, a Vector-Analytic Solution		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 0: Why Vector Calculus?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of e²ˣ/(еˣ+1) - Integration by Substitution, Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of 1/(eˣ + e⁻ˣ) - Integration by Substitution, Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of 1/(1+√x) - Integration by Substitution, Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of x⁷/√(1+x⁴) - Integration by Substitution, Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of (1+x)/(1+x^2) - Integration by Substitution, Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of tan(x) - Integration by Substitution, Calculus 2	tan(x) 的积分 - 换元积分法, 微积分 2	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Nothingburger integrals involving the natural logarithm - Integration by Substitution, Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
5. x⁵ √(x³+7)- Integration by Substitution, Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Foreword to Integration by Partial Fractions (No examples in this video)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of 1/(x²-1), Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of (x-1)/(x²-4x-12), Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of (6x+12)/(x²+x), Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of 1/ (x²+4x+5), Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of (2x+3)/x(x-1)², Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of x³/( x²+1), Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of 1/(x³+x²+x+1), Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of (ln x + 1)/x ln x (1 + ln²x), Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of 1/(e²ˣ-1), Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integration by Partial Fractions, Integral of 1/sin² x cos x, Calculus 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of x³/(x² + 1) - Watch "USSR vs USA Integration by Substitution" first!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of 1/√x(1+x) - Watch "USSR vs USA Integration by Substitution" first!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of sin⁷x cos x / (21 + sin⁸x) - Watch "USSR vs USA Integration by Substitution" first!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of e^√x / 2√x cos²(e^√x) - Watch "USSR vs USA Integration by Substitution" first!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
USSR vs USA Integration by Substitution		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of (m+1)/(m²+1)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of (s+1)√(s-1)√(s+3)	(s+1)√(s-1)√(s+3) 的积分	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Integral of 1/(y+y ln^2 y)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of z²/(z²+1)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Roman and Anastasia show us how it's done	罗马和安娜斯塔西娅向我们展示了怎么做。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Integral of z²/(z+1)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of (√x + 1)^2	(根号x加一)的平方的积分	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Integral of (2x+1)/sqrt(x)sqrt(x+1)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of 1/cos x sin x		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of x sqrt(x+1)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of 1/(1+2x+x²)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: Integral of 1/(2+2x+x²)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of 1/(3+5x²)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of 1/(1+5x²)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Integral of Sin(2x-3)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Simple Shifts in Indefinite Integrals	不定积分中的简单平移	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Calculus 2: The Integral of x³/(1+x⁸) and the Integral of x⁷/(1+x⁸)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of 1/(x ln x)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of ln x / x		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of ln²x / x		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of x³/√(1+7x⁴) and the Right Way to Think about Integration by Substitution		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of sin⁶x cos x and the Right Way to Think About Integration by Substitution		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Integral of x⁹cos x¹⁰ and the Right Way to Think About Integration by Substitution		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: Integration by Substitution - Let's Warm up by Using the Chain Rule!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of 1/√x		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of a Fractional Exponent in the Denominator by the Power Law		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of tan⁶x/cos²x and a Rant Against Secants!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: Integration by the Sum Rule and Integration of Polynomials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of a Fractional Exponent by the Power Law		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of 1/x and a Rant Against Absolute Values		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Integral of a Negative Exponent by the Power Law		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: Integral of 3x⁷ by the Power Law		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Right Way to Think About Integration Technique (Integral of x³ by the Power Law)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: Positive and Negative Area Conventions and the Fundamental Theorem of Algebra		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Fundamental Theorem of Calculus in the Definite-Integral Form		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The FTC and the Integral of e⁵ˣ from 1 to 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The FTC and the Integral of eˣ from 0 to 1		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Only Way to Integrate Is by Guessing!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: Welcome!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Calculus 2: The Fundamental Theorem of Calculus (...is not a theorem)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
An Alert for My Tensors Textbook		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
https://lem.ma/Calculus - Free AP Calculus Prep Tool - Spread the Word!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 19: Derivative of a Constant-Length Vector		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 21: Torricelli's Problem, a Vector-Analytic Solution		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 18: The Unit Tangent Vector		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 13: Projection onto a Subspace		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 17: The Derivative of a Vector Function Is the Tangent to the Curve		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 16: All Vector Functions Correspond to Curves in Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 15: Differentiation of Vectors - Finally!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 14: The Dot Product Matrix Is Positive Definite		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Self-Adjoint Transformations	自伴随变换	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Vector Calculus 5a: A Clarification of Weighted Averages of Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
How I Came to Terms with Complex Numbers		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 11: Triangle Bisector in Terms of the Dot Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 10: Orthogonal Projection in Terms of the Dot Product. Also, Rejection.		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 9: The 3 Definitions of the Dot Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 12: Linear Decomposition by the Dot Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 7: Triangle Medians Are Concurrent, a Vector Algebra Proof		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 8: Why the Dot Product? ...and Its Essential Properties		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 6: The Triangle Midsegment Theorem		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 5: Vector Equation of a Straight Line		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 4: The Essential Properties of Vector Addition and Multiplication		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 3: Vector Multiplication by a Number		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 2: Vector Addition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Vector Calculus 1: What Is a Vector?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear ODEs with Constant Coefficients: Repeated Roots		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear ODE with Constant Coefficients: Complex Roots with Nonzero Real Parts		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear ODE with Constant Coefficients: The Homogenized Equation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Component Space Representation of Inner Products		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
What Is Lemma?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Announcing the SAT Math Platform by Lemma		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7f1: Null Space of a Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
AP Calculus Practice Tool - Please Help Spread the Word - lem.ma/2S		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A Man Bought A Goat: A Surprisingly Confusing Question		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Non-Newtonian Fluids in Action	非牛顿流体在行动	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Solution of the Laplace Equation on an Annulus		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Laplace Eigenvalues on the Unit Disk: A Complete Derivation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Solving the Wave Equation in 1D by Fourier Series	利用傅里叶级数求解一维波动方程	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Solution of the Poisson Equation on Unit Disk	单位圆盘上泊松方程的解	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
A Few Words about the Infinite Fourier Series	关于无穷傅里叶级数的几句话	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Inner Products With and Without Component Spaces		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Fourier Series Is Nothing but a Least Squares Problem!	傅里叶级数无非是一个最小二乘问题。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Solving the Heat Equation in 1D by Fourier Series		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A Criterion for Positive Definiteness of a Symmetric Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Location of Minima and Maxima in Functions of Several Variables	多变量函数中最小值和最大值的位置	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
The Surprising History of Stellar Parallax	恒星视差的令人惊讶的历史	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Laplace Eigenvalues on the Rectangle: A Complete Derivation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Decomposition by Inner Product in the Underdetermined Case and Least Squares	欠定情况下的内积分解与最小二乘	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Derivation of Poisson's Formula for of Laplace's Equation on the Unit Disk: Complex Fourier Series!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Laplace Equation on the Unit Disk	单位圆盘上的拉普拉斯方程	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Decomposition by Inner Product with General Bases	基于一般基的内积分解	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Complex Fourier Series	复数傅里叶级数	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Identifying Minima and Maxima in Multivariable Calculus: The Second Derivative Criterion		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A 3x3 Symmetric Eigenvalue Decomposition in under 3 Minutes!	不到 3 分钟完成 3x3 对称特征值分解！	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
A Symmetric Eigenvalue Decomposition Example in under Three Minutes!	一个对称特征值分解的例子，在不到三分钟内！	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Eigenvectors of Symmetric Matrices Are Orthogonal	对称矩阵的特征向量是正交的	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
A (Silent) Least Squares Example	一个 (无声) 最小二乘示例	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
The Least Squares Formula: A Derivation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Quadratic Form Minimization: A Calculus-Based Derivation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The LDU and LDLᵀ Decompositions and the Implications for Positive Definiteness	LDU 和 LDLᵀ 分解以及对正定性的意义	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
For a Positive Definite M, Is BᵀMB Always Positive Definite, Too?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Fourier Series: Preliminary Remarks		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Fourier Series for f(x) = x	f(x) = x 的傅里叶级数	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Fourier Series: What to Expect		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Fourier Series: Determining the Coefficients		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Fourier Series for f(x) = π² - x²	f(x) = π² - x² 的傅里叶级数	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
The Most Important Video in the Series: The Linear Property of the Fundamental PDEs		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Solving the Heat Equation in 1D and the Need for Fourier Series	求解一维热方程以及傅里叶级数的必要性	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
PDEs: Separation of Variables Step 2, Which Is Putting It All Together!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
PDEs: Separation of Variables		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A Riddle: What watershed event in the history of mathematics does this poem represent?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Is BᵀB Always Positive Definite? (Also, Messi makes a comeback!)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Charlie Chaplin Wannabe Wins an Oscar for Least Squares	卓别林模仿者凭借最小二乘法赢得奥斯卡奖	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
General Inner Products in ℝⁿ. Matrix Representation	ℝⁿ 上的广义内积。矩阵表示。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Solving Poisson's equation in 1D	求解一维泊松方程	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Solving the Laplace Equation in 1D	求解一维拉普拉斯方程	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
A Further Introduction to the Wave Equation	进一步介绍波动方程	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Introduction to the Heat Equation	热方程引论	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Introduction to Laplace and Poisson Equations	拉普拉斯方程和泊松方程介绍	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Orthogonal Matrices	正交矩阵	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
What Is the Laplacian?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
An Ode to the Second Derivative	二阶导数颂歌	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
The QR Decomposition	QR分解	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Gram-Schmidt in ℝ³	ℝ³ 中的格拉姆-施密特	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Gaussian Quadrature 3: The Explanation of the Technique		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Gaussian Quadrature 2: How to Determine the Weights		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Gaussian Quadrature 1: Summary of Legendre Polynomials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Why {1,x,x²} Is a Terrible Basis	为什么 {1,x,x²} 是一个糟糕的基底	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Gram-Schmidt Orthogonalization and Legendre Polynomials	格拉姆-施密特正交化和勒让德多项式	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Decomposition with Respect to Legendre Polynomials	关于勒让德多项式的分解	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Gram-Schmidt Orthogonalization for Three or More Vectors	用于三个或更多向量的 Gram-Schmidt 正交化	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Gram-Schmidt Orthogonalization via an Algebraic Way of Thinking	通过代数思维方式的格拉姆-施密特正交化	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Introduction to the Gram-Schmidt Orthogonalization Procedure	格拉姆-施密特正交化过程介绍	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
A Lemma Challenge: Solve the Conundrum of Near Resonance!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear ODEs: Resonance and Repeated Roots		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Intuitive Explanation of Resonance by Helmholtz	亥姆霍兹对共振的直观解释	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear ODEs with Constant Coefficients: Classical Resonance		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear ODEs with Constant Coefficients: Illustration of Resonance with Exponentials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Overview of Resonance Phenomena	共振现象概述	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
World's Simplest ODE is Still Interesting!	世界上最简单的常微分方程仍然很有趣！	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear ODEs with Constant Coefficients: The Harmonic Oscillator		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
"Almost Inner Products" on the Space of Polynomials	几乎内积在多项式空间上	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Inner Products in ℝⁿ	ℝⁿ 中的内积	MathTheBeautiful - Videos	美丽数学 - 视频	MathTheBeautiful	原始链接
Linear ODEs with Constant Coefficients: Matching the Initial Conditions		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
What Are Orthogonal Polynomials? Inner Products on the Space of Functions		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear ODEs with Constant Coefficients: Distinct Roots		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A Brief Recap + Inner Products for Geometric Vectors	简要回顾 + 几何向量的内积	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
PDEs 4: Linear ODEs with Constant Coefficients, Finding a Particular Solution		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
PDEs 3: A Linear ODE Is Nothing but Ax=b, and That's THE Most Important Point!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Inner Product is Dot Product, Turned on Its Head	内积是点积，只不过是颠倒过来了。	MathTheBeautiful - Videos	美丽数学 - 视频	MathTheBeautiful	原始链接
Review of Decomposition by the Dot Product	点积分解的回顾	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Review of the Dot Product	回顾点积	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
PDEs 2: Why ODEs Are Easy:They Are Just Like a Treasure Hunt!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
PDEs 1: The Lay of the Land		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Introducing the Inner Product - A Fundamental Concept in Linear Algebra	引入内积——线性代数中的一个基本概念	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 14TBD: Row or Column Expansion of the Determinant by Cofactors (or Minors)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Complete Proof of the Product Property of the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Determinant-Based Derivation of the Triangle Area Formula		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Area of a Triangle as a Function of Its Cartesian Coordinates		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: An Application of the Product Property of the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The Product Property of the Determinant - Proof for Elementary Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Calculation of Areas and Volumes by the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Calculation of the Determinant by Gaussian Elimination		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: An Elegant Approach to Defining the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The Determinant is Zero ⇔ Matrix Is Singular		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The Linear Property of the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The Effect of Adding a Multiple of One Row to Another on the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The Alternating Property of the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The Direct Algebraic Definition of the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The Determinant of a Triangular Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The Transpose Property of the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Overview of the Properties of the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Straw Trick	吸管把戏	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Linear Algebra 14a: Why Determinants?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Determinant Zen	决定性的禅	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Tyrone Who Sings on the Subway	在地铁上唱歌的泰隆	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 16h8: Defective Transformations!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16h7: Generalized Eigenvectors Example		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16h6: Generalized Eigenvectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16h5: Defective Transformations?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16h4: Defective Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16h3: Algebraic Multiplicity Matches Geometric Multiplicty		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16h2: Repeated Eigenvalues and the Algebraic Multiplicity		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16h1: Repeated Eigenvalues and the Geometric Mulitplicity		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Setting the Stage for the NxN Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Derivation of the 3x3 Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Interesting 2x2 Determinant Examples		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Derivation of the 2x2 Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7g: The Nullspace of a 3x3 Matrix with a Specific Pattern		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
My daughter meets the legendary Irving Fields	我的女儿遇见了传奇的Irving Fields。	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra Challenge: Evaluate the Power of a Matrix in Your Head		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: The 3x3 Determinant - A 2nd Illustration		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11L5: The Column Space of AB		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Calculating the 3x3 Determinant the Indian Way		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Calculating the 3x3 Determinant the American Way		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Calculating the 3x3 Determinant the Russian Way		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14TBD: Three Ways of Calculating the 3x3 Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Sum of Polynomial Coefficients Challenge	多项式系数之和挑战	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 9q: Gaussian Thinning		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11L3: The Null Space of the Product AB, Proof by Matrix Algbra		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11L4: The Relationship Between the "Old" and the "New" Expressions for the Null Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7d1: Linear Dependence by Simple Counting		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9p: Pragmatic Gaussian Elimination		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9c1: Gaussian Elimination Cannot Be Used to Determine the Column Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11L1: A Matrix Algebraic Expression for the Null Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11L2: The Null Space of the Product AB		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 4d1: A Property Irrelevant in Decomposition Problems		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7d2: A Potential Pitfall Determining the Span		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Simplest Irrational Number	最简单的无理数	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Pennies from Heaven	天降财神	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Stairway to Heaven	天堂的阶梯	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
What's John's Favorite Number?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Can an Irrational Number to Irrational Power be Rational?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Knight's Tour	马踏棋盘	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 11ya: The Inverse of the Transpose		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
The Chessboard Problem	棋盘问题	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 17g: Easy Eigenvalues - The Transpose		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16c2: A and Aᵀ Have the Same Eigenvalues		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Water and Wine	水和酒	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 4e: Linear Subspaces in ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 4g: A Good Way to Express Linear Subspaces in ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 4h: Unions and Intersections of Linear Subspaces		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 4f: Linear Subspaces of Polynomials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 4d: What is a Linear Property and Why It's Synonymous with Subspace		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 4c: Impossible Decomposition in ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 4b: Impossible Decomposition with Polynomials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 4a: Impossible Decomposition with Geometric Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3e: Linear Systems Are a Decomposition Problem		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3d3: Decomposition in ℝⁿ, 3		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3d2: Decomposition in ℝⁿ, 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3d1: Decomposition in ℝⁿ 1		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3c2: Decomposition with Polynomials 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3c1: Decomposition with Polynomials 1		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3b4: Decomposition with Respect to Arbitrary Geometric Vectors, Affine Grid		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3b3: Decomposition with Geometric Vectors 3		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3b2: Decomposition with Geometric Vectors 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3b1: Decomposition with Geometric Vectors 1		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 3a: What is Linear Decomposition?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Entering General Solutions on Lemma	进入关于引理的通解	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 2g: Subtraction of Geometric Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2ga: Subtraction is Often Easier than Addition!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2ia: Is One Polynomial a Multiple of the Other?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11zc: The Combination x ᵀAy for a Symmetric matrix A		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algabra 11zb: The Combination xᵀAy		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11za: The product A ᵀA is Always a Symmetric Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11z: Introduction to Symmetric Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11y: The Transpose of a Triple Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11x: The Transpose of a Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11w: Introduction to the Transpose of a Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 23g: SVD Proof That the Orthogonal Matrices in Alternative Polar Decompositions Match		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 23f: Introducing the Celebrated Singular Value Decomposition (SVD)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 23d: Demonstration That AᵀA and AAᵀ Have Identical Eigenvalues		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 23c: A Worked out Polar Decomposition Example		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 23b: How to Determine the Matrices Q and S in the Polar Decomposition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 23e: Reversing the Multiplicative Terms in the Polar Decomposition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 23a: Polar Decomposition - A Product of an Orthogonal and Symmetric Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22g: Geometric Interpretation of the Eigenvalue Decomposition for Symmetric Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21j: Two Geometric Interpretations of Orthogonal Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20f: The Product of Two Orthogonal Matrices Is Itself an Orthogonal Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22i: Symmetric Matrices and the LDU Decomposition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22a: Introduction to Orthoscaling (aka Symmetric) Transformations		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22h: Is the Inverse of a Symmetric Matrix Itself Symmetric?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22j: The Cholesky Decomposition and a Tribute to Land Surveyors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22c: Symmetric Matrices Have Orthogonal Eigenvectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22d: Symmetric Matrices (Even with Repeated Eigenvalues) Have Orthogonal Eigenvectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22b: Orthoscaling Transformations Are (Sometimes) Represented by Symmetric Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22e: The Symmetric Property as a New Eigenvalue Giveaway		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 22f: Symmetric Matrices and the Eigenvalue Decomposition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21f: Rotation Matrices in 3D for Rotations with respect to the Coordinate Axes		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21g: Euler Angles and a Short Tribute to Leonhard Euler		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21h: The Matrix that Represents an Arbitrary Rotation in 3D		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21i: How to Represent a Rotation with respect to an Arbitrary Axis		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19r: Translations, or How to Represent Nonlinear Transformations by Matrix Products		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19s: The Concept of Basis Orientation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21e: What All 2x2 Orthogonal Matrices Look Like		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21d: Rotation Matrices in a Non-Cartesian Basis		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21c: Rotation Matrices - Or Why You Should Love Trig		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21b: Rotations, Plane and Simple!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 21a: Rigid Transformations		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20L: The Dot Product in Non-Cartesian Bases, the Gram Matrix or the Metric		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20k: Two Derivations of the Dot Product Component Space Expression		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20j: The Dot Product, Matrix Multiplication, and the Magic of Orthogonal Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20i: Component Representation of the Dot Product, as if You Don't Know It Already		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20h: The Key Properties of the Dot Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20g: The Dot Product - One of the Most Brilliant Ideas in All of Linear Algebra		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20e: Proof that Length Preservation Implies the Orthogonal Matrix Property		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20d: Length Preserving Linear Transformations and Orthogonal Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20c: Length Expressed in a non-Cartesian Basis		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20b: Length Expressed in Terms of Components of a Vector		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 20a: Introduction to Transformations (Mostly Linear) in the Plane and in the 3D Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2n: Spanning Sets		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2m: Span the Man		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2i: Polynomials Are Vectors, Too!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2j: Elements of ℝⁿ as Vectors - So Boring, yet so Important!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2k: Linear Combinations - a New Term for an Old Concept		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2L: The Zero Vector - Does Nothing, Yet so Important!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2h: What Else Works like Geometric Vectors?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2g: Subtraction of Geometric Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2f: The Origin in the Plane and the Parallelogram Rule		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2e: Confirming All the 'Tivities		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2e: Confirming All the 'Tivities		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2d: Addition of Geometric Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2c: The Three Fundamental Examples of Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2a: J.S. Bach + M.L. King = Linear Algebra, or the Addition of Sounds		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Decomposition	线性分解	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Linear Algebra 19t: I Once Was Blind, but Now Am Dilated		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19u: The Derivative Operator Is Defective		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19s: A Moment for Reflection... Eigenvalues		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8k: You and I Have a Problem - We Need Some Distance!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19k: Matrix Representation of a Linear Transformation - Vectors in ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19e: Illustration of Component Spaces by a Sum of Vectors in ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15m+: The Identity Crisis, I Mean, Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19f: The Heart of Component Spaces - Matrix Representation of a Linear Tranformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19i: Bad Basis! Bad Basis! Go to Your Room!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19b: Component Spaces - Doing It Right!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19p: Proof that Eigenbasis Yields a Diagonal Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19n: Matrix Representation of a LT - Vectors in ℝⁿ, Second Example		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19d: Illustration of Component Spaces by a Sum of Polynomials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19j: Matrix Representation of a Linear Transformation - Polynomials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19o: Matrix Representation of a LT - Better than an Eigenbasis?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19q: Matrix Representation of a LT - The Identity Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19h: Matrix Representation of a Linear Transformation - Alternative Basis		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19c: Illustration of Component Spaces by a Sum of Geometric Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19L: Matrix Representation of a LT - Vectors in ℝⁿ, Standard Basis		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19g: Matrix Representation of a LT - the Algorithm Works!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19m: Matrix Representation of a LT - Vectors in ℝⁿ, Eigenbasis		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Preview: The Magic of Gaussian Quadrature - A Billion Times Better than the Next Best Thing		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 19a: Component Spaces - What They Are for and When to Use Them		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A Complete In-Depth Linear Algebra Course with Problems and Exercises	完整深入的线性代数课程，附带习题与问题	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 11s+: The Order of Operations Doesn't Matter When Computing the Inverse by RREF		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 12b: Applications Series - Non-Polynomial Interpolation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 12a: Applications Series - Polynomial Interpolation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 12c: Applications Series - Polynomial Interpolation According to Lagrange		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Response to Eben	回复 Eben	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 9c-: Review - Column Space Versus Null Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16L: Similarity Transformations Preserve the Trace and the Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus 4f: The Relationship Between the Covariant and the Contravariant Bases		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 14a: Determinants		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16c1: The Sum is the Trace and the Product Is the Determinant of the Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 18e: The Eigenvalue Decomposition and Fibonacci Numbers		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 18d: The Eigenvalue Decomposition and Powers of a Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 18c: An Important Implication of the Eigenvalue Decomposition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 18b: A Worked out Eigenvalue Decomposition Example		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 18a: Introduction to the Eigenvalue Decomposition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17f: Easy Eigenvalues - The Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17i: Easy Eigenvalues - The Grand Finale		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17h: Easy Eigenvalues - The Block Diagonal Structure		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17e: Easy Eigenvalues - The Trace		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17d: Easy Eigenvalues - Nontrivial Null Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17c: Easy Eigenvalues - Equal Sums of Rows or Columns		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17b: Easy Eigenvalues - Diagonal Entry - A Single Nonzero Entry in a Column		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17a: Easy Eigenvalues - Diagonal Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 17j: Constructing a Matrix with a Prescribed Spectrum		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16m: Eigenvalues, Eigenvectors and the Square Root of a Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16k: Eigenvalues, Eigenvectors and the Similarity Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16j: Eigenvalues and Eigenvectors of the Square and the Inverse		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16n: Every Matrix Satisfies Its Characteristic Equation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16g: Eigenvalues and Eigenvectors Example - A 3x3 Triangular Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16f: Eigenvalues and Eigenvectors Example - No Real Eigenvalues		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16e: Eigenvalues and Eigenvectors Example with Radicals		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16d: Eigenvalues and Eigenvectors - A 2x2 Example		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16c: Determining Eigenvalues and Eigenvectors, a Detailed Example		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16b: Algebraic Derivation of the Eigenvalue Algorithm		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 16a: The Eigenvalue Algorithm		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Proofs 15b: Eigenvectors with Different Eigenvalues Are Linearly Independent		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Proofs 15a: Eigenvectors with the Same Eigenvalue Form a Linear Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15p: The Inverse of a Linear Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15o: The Null Space of a Linear Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15m: All Transformations in ℝⁿ Can Be Represented by Matrix Products		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15n: Why Eigenvalues and Eigenvectors Are So Important!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15L: Another Linear Transformation in ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15k: A Linear Transformation in ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15j: Example of Nonlinear Transformations of Functions		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15i: Dilation as a Linear Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15h: The Derivative as a Linear Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15g: Geometric Transformation in Space, As Opposed to on the Plane		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15f: The Transformation of Translation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15e: The Rotation Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15d: The Projection Transformation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15c: The Reflection Transformation and Introduction to Eigenvalues		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 15b: What Makes a Transformation Linear?		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11v: A Fascinating Matrix Product That Anticipates Rotations		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 13g: Third Explanation of the Matrix Inversion Algorithm		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 13f: An LU Decomposition Example		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11u: Two Interesting Matrix Product Examples		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Proofs 11d: Left Inverse Is Right Inverse - A and A^-1 Commute		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 13a: Introduction to Elementary Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 13e: The LU Decomposition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 13d: Elementary Matrix Exercises		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 13c: The Inverse of an Elementary Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 13b: The Effect of an Elementary Matrix on the Other Matrix in a Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11t: The Inverse of a Product of Two Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11s: An Even Better Explanation for the Inversion Algorithm Based on RREF		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11r: First Explanation for the Inversion Algorithm		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11q: Algorithm for Calculating the Inverse Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11p: Some Matrices Are Not Invertible - I.e. They Don't Have an Inverse		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11o: There Is Only One Inverse Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11n: The Inspired Idea of the Matrix Inverse		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11m: The Identity Matrix - The Number One of Matrix Algebra		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11L: The Three Equivalent Perspectives on Matrix Multiplication		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11k: The Commutative Property of Matrix Multiplication - Or Lack Thereof!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11j: The Associative Property (a.k.a. Associativity) of Matrix Multiplication		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11h: A Few Matrix Multiplication Examples		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11g: Complete Definition of Matrix Multiplication for Arbitrary Compatible Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11f: An Example of an Incompatible Matrix Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11d: Matrix Products as Actions		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11c: Definition of Matrix Multiplication for Single Columns on the Right		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11b: A Look Ahead - An Illustration of Matrix Algebra		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11a: Introduction to Matrix Multiplication and Matrix Algebra		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 11e: A Few Matrix Product Examples with Crooked Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Coming to Terms with Infinities: The Area Challenge		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 10f: The RREF of a Matrix Whose the Null Space is Known Beforehand		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 10d: The Rank of a Matrix - A Spectacular Application of the Row Echelon Form (RREF)		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 10e: An Application of the Matrix Rank		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 10c: A Row Reduced Echelon Form (RREF) Challenge		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 10b: Calculating the Null Space from the Row Reduced Echelon Form (RREF) of a Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 10a: Introduction to the Row Reduced Echelon Form (RREF) of a Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7f2: 21 Easy Null Space Exercises		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9o: Gaussian Elimination Example 7		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9n: Gaussian Elimination Example 6		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9m: Gaussian Elimination Example 5		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9L: Gaussian Elimination Example 4		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9k: Gaussian Elimination Example 3		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9j: Gaussian Elimination Example 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9i: Gaussian Elimination Example 1		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Comment: Reusing the Same Letter in Different Expressions		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9g: Which Columns Are Pivot Columns in Gaussian Elimination		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9f: Row Switching in Gaussian Elimination		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9e: Gaussian Elimination and Systems Without Solutions		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9d: First Gaussian Elimination Example		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9c: Why Gaussian Elimination Works		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9b: The Operations of Gaussian Elimination		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 9a: Introduction to Gaussian Elimination		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8j: The Simplest Possible System		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8i: An Exceedingly Simple Linear System		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8p: The Relationship Between the Column Space and the Null Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8h: A Linear System with Zero Columns		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8g: A Wide Linear System		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8f: A Tall Linear System		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8e: A 3x3 Linear System		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8d: Another 2x4 Linear System		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8c: Linear Systems as Collections of Equations - Not Such a Great Perspective		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8b: Our First Linear System - A Thorough Discussion		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 8a: Linear Systems Terminology		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6k: The Null Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7e: Counting Solutions of a Linear System		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6da: Linear Independence Implies Uniqueness		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7d: Relationship among Four Quadratic Polynomials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7c: Concepts of Basis and Dimension		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7b: Four Linearly Independent Vectors in the Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 7a: Three Linearly Independent Vectors in the Plane		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6z: Outtakes from Chapters 5 and 6		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6j: Linear Systems for the Impatient		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6i: Linear Dependence Example 5 - Vectors in ℝⁿ		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6h: Linear Dependence Example 4 - Polynomials		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6g: Linear Dependence Example 3 - Geometric Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6f: Linear Dependence Example 2 - Geometric Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6e: Linear Dependence Example 1 - Geometric Vectors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6d: The Equivalence of the Two Definitions of Linear Dependence	线性代数 6d 线性相关的两个定义的等价性	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Linear Algebra 6c: Second Definition of Linear Dependence Fixed!	线性代数 6c 第二个线性相关定义已修正!	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra 6b: Alternative Definition of Linear Indpendence		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 6a: Linear Independence		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2o3: Equation of a Straight Line - More Important than You'd Think!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra: Chapters 1 - 4 Outtakes - as funny as your calculus professor		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2o2: Straight Talk - a Linear Combination Exercise		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2o1: Linear Subspaces of the Plane		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2k1: Examples of Linear Combinations		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2q: Summary of Terms Encountered so Far		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2p: A Passionate Appeal - Treat All Objects on Their Own Terms!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra 2k2: Linear Systems Are a Decomposition Problem		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
A Vector Calculus Challenge: Area and Volume as Boundary Integrals		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 15: Geodesic Curvature Preview		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 14f: Principal Curvatures		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 14e: Non-hypersurfaces - Relationship Among Curvature Tensors 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 14d: Non-hypersurfaces - Relationship Among Curvature Tensors 1	张量微积分讲座 14d - 非超曲面 - 曲率张量之间的关系 1	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 14c: Non-hypersurfaces - Relationship Among The Shift Tensors	张量微积分讲座 14c 非超曲面 - 转移张量之间的关系	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 14b: Examples of Curves in 3D		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 14a: Non-hypersurfaces	张量微积分讲 14a 非超曲面	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 13b: Integration - The Divergence Theorem		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 13a: Integration - The Arithmetic Integral		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus 12c: The Self-Adjoint Property in Tensor Notation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 12b: Inner Products in Tensor Notation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 12a: Linear Transformations in Tensor Notation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 10c: The Second Order Normal Derivative		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 3g: Easy Eigenvalues - The Determinant		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 3e: Easy Eigenvalues - The Trace	线性代数 3e小节简单特征值 - 迹	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra Vignette 3h: Easy Eigenvalues - The Grand Finale		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 3d: Easy Eigenvalues - Linearly Dependent Columns	线性代数小插曲 3d 简单的特征值 - 线性相关的列	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra Vignette 3c: Easy Eigenvalues - Sums Of Rows		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 4c: Fibonacci Numbers - The Derivation Of The Formula		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 4b: Fibonacci Numbers As A Matrix Product		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 4a: Fibonacci Numbers - Review Of The Eigenvalue Decomposition		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 3b: Easy Eigenvalues - Diagonal Entry		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 3e: Easy Eigenvalues - Triangular Matrices		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 3a: Easy Eigenvalues - Introduction		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 11b: Gauss' Theorema Egregium, Part 2		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 11a: Gauss' Theorema Egregium, Part 1		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 10b: The Normal Derivative		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 2e: RREF - Back To The Null Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 2d: RREF And The Inverse Matrix		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 2b: RREF - Why It Works		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 2c: RREF - When It's Easy!		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Linear Algebra Vignette 2a: RREF - What It's For		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 10a: The Covariant Surface Derivative in Its Full Generality	张量微积分第10a讲完全一般性下的协变曲面导数	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra Vignette 1c: Why It Works	线性代数专题 1c 为何奏效	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra Vignette 1: Saying Hello	线性代数片段 1 打招呼	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra Vignette 1b: The Dilation Operator (Has Important Applications)	线性代数小短文 1b 伸缩算子（有重要应用）	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Linear Algebra Vignette 1a: Matrix Representation of a Linear Transformation	线性代数片段 1a 线性变换的矩阵表示	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Derivative of a Basis Vector Illustrated (e_r in polar coordinates)	图解基向量的导数 (极坐标下的 e_r)	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 9b: The Components of the Normal Vector	张量微积分第9b讲法向量的分量	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 9a: The Equations of Surface and the Shift Tensor	张量微积分第9a讲曲面方程和位移张量	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 8e: The Riemann Christoffel Tensor & Gauss's Remarkable Theorem	张量微积分第8e讲黎曼-克里斯托费尔张量与高斯绝妙定理	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 8c: The Curvature Tensor On The Sphere Of Radius R	张量微积分讲座 8c：半径为 R 的球面上的曲率张量	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 8b: The Surface Derivative of the Normal	张量微积分第8b讲法线的表面导数	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Tensor Calculus 8d: The Christoffel Symbol on the Sphere of Radius R	张量微积分 8d 半径为R的球面上的克里斯托费尔符号	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 8: Embedded Surfaces and the Curvature Tensor	张量微积分第8讲嵌入曲面和曲率张量	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 7d: The Voss-Weyl Formula	张量微积分第7d讲 Voss-Weyl 公式	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 7c: The Levi-Civita Tensors		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus Lecture 7b: Relative Tensors	张量微积分讲座 7b 相对张量	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 7a: Determinants and Cofactors	张量微积分第7a讲行列式和余子式	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus 4b: Position Vector, Covariant Basis, Covariant Metric Tensor, Contravariant Basis		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus 6d: Velocity, Acceleration, Jolt and the New δ/δt-derivative	张量微积分六维速度、加速度、急动度和新的 δδt 导数	MathTheBeautiful - Videos	美妙的数学 - 视频	MathTheBeautiful	原始链接
Tensor Calculus Lecture 6c: The Covariant Derivative 2	张量微积分第6c讲协变导数 2	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus 5b: Invariants Are Tensors	张量微积分 5b 不变量是张量	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus 6b: The Covariant Derivative	张量微积分 6b 协变导数	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Tensor Calculus 6a: The Christoffel Symbol	张量微积分 6a 克里斯托费尔符号	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus 4g: Index Juggling	张量微积分 4g 索引腾挪	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Tensor Calculus 4e: Decomposition by Dot Product in Tensor Notation	张量微积分第四版在张量记号中的点积分解	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus 4d: Quadratic Form Minimization	张量微积分四维二次型最小化	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus 5a: The Tensor Property		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus 4c: A Few Tensor Notation Exercises	张量微积分 4c：一些张量记号习题	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus 4a: The Tensor Notation		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus 2b: Two Geometric Gradient Examples (Torricelli's and Heron's Problems)	张量微积分 2b 两个几何梯度例子 (托里拆利问题和海伦问题)	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Tensor Calculus 3a: The Covariant Basis		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Tensor Calculus 2: The Two Conflicting Definitions of the Gradient		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Geometric vectors as the starting point for Tensor Calculus. Vector-valued functions and more!	几何向量作为张量微积分的起点。向量值函数等等！	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Why Tensor Calculus?	为什么张量微积分	MathTheBeautiful - Videos	美丽的数学 - 视频	MathTheBeautiful	原始链接
Special Eigenvalue Features: Introduction		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Eigenvalue Feature 4: The Trace		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Eigenvalue Feature 3: Nontrivial Null Space		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Eigenvalue Feature 2: Sums of Rows	特征值特征2 行和	MathTheBeautiful - Videos	数学之美 - 视频	MathTheBeautiful	原始链接
Eigenvalue Feature 1: Single Nonzero Entry in a Column		MathTheBeautiful - Videos		MathTheBeautiful	原始链接
Algebra 14 \| Cyclic Groups		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 13 \| Conjugate Subgroups [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 19 \| Covariance and Correlation [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 19 \| Covariance and Correlation		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 13 \| Conjugate Subgroups		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 15 \| Proof of Uniform Convergence [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 15 \| Proof of Uniform Convergence		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 14 \| Uniform Convergence of Fourier Series [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 14 \| Uniform Convergence of Fourier Series		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 17 \| Convolution with Distributions of Compact Support [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 17 \| Convolution with Distributions of Compact Support		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 16 \| Distributions with Compact Support [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 16 \| Distributions with Compact Support		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 7 \| Approximation Formula [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 7 \| Approximation Formula		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 6 \| Orthogonal Complement [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 6 \| Orthogonal Complement		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 32 \| Example for General Linear Equation [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 32 \| Example for General Linear Equation		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 15 \| Support for Distributions [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 15 \| Support for Distributions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 31 \| Solutions for Linear Equations [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 31 \| Solutions for Linear Equations		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 5 \| Proof of Jordan-von Neumann Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 5 \| Proof of Jordan-von Neumann Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 4 \| Parallelogram Law [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Webster Method (German Election System - Bundestag 2025)	韦伯法 (德国选举制度 - 联邦议院 2025)	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Hilbert Spaces 4 \| Parallelogram Law		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Thank you for 200k subscribers!!!	感谢 20 万订阅者!!!	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 31 \| Central Limit Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 31 \| Central Limit Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multidimensional Integration 5 \| Change of Variables Formula [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multidimensional Integration 5 \| Change of Variables Formula		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 43 \| Integral is Well-Defined [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 43 \| Integral is Well-Defined		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 30 \| Similar Matrices [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 30 \| Similar Matrices		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
German Election System - Bundestag 2025 - New Voting System Explained [dark version]	德国选举制度 - 联邦议院 2025 - 新投票制度解释 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 29 \| Rank gives Equivalence [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 29 \| Rank gives Equivalence		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 28 \| Equivalent Matrices [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 28 \| Equivalent Matrices		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 30 \| Strong Law of Large Numbers [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 30 \| Strong Law of Large Numbers		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multidimensional Integration 4 \| Fubini's Theorem in Action [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
German Election System - Bundestag 2025 - New Voting System Explained	德国选举制度 - 2025年联邦议院 - 新选举制度解释	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Multidimensional Integration 4 \| Fubini's Theorem in Action		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 27 \| Change of Basis for Linear Maps [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 27 \| Change of Basis for Linear Maps		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 29 \| Monte Carlo Integration		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 29 \| Monte Carlo Integration [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 16 \| Proof of the Substitution Rule for Measure Spaces [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 28 \| Weak Law of Large Numbers [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 28 \| Weak Law of Large Numbers		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 27 \| kσ-intervals [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 27 \| kσ-intervals		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Update for 2025 - More Maths Must Be Made	2025 年更新 - 必须做出更多数学成果	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Hilbert Spaces 2 \| Examples of Hilbert Spaces [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 2 \| Examples of Hilbert Spaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multidimensional Integration 2 \| The n-dimensional Lebesgue Measure [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multidimensional Integration 2 \| The n-dimensional Lebesgue Measure		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 13 \| Fourier Series Converges in L² [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 13 \| Fourier Series Converges in L²		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 31 \| Lagrangian [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 31 \| Lagrangian		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 30 \| Example for Lagrange Multipliers [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 30 \| Example for Lagrange Multipliers		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 29 \| Method of Lagrange Multipliers [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 29 \| Method of Lagrange Multipliers		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fundamental Theorem of Calculus \| Expansion of the Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fundamental Theorem of Calculus \| Expansion of the Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 28 \| Extreme Values With Constraints [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 28 \| Extreme Values With Constraints		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multidimensional Integration 1 \| Lebesgue Measure and Lebesgue Integral [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multidimensional Integration 1 \| Lebesgue Measure and Lebesgue Integral		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 27 \| Application of the Implicit Function Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 27 \| Application of the Implicit Function Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 26 \| Matrix Representations for Compositions [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 26 \| Matrix Representations for Compositions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 12 \| Subgroups under Homomorphisms [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 12 \| Subgroups under Homomorphisms		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 11 \| Klein Four-Group [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 11 \| Klein Four-Group		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 10 \| Subgroups [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 10 \| Subgroups		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 21 \| Solution Set of Linear ODEs [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 21 \| Solution Set of Linear ODEs		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 20 \| Matrix Exponential [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 20 \| Matrix Exponential		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 19 \| Solution Space [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 19 \| Solution Space		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 9 \| Group Homomorphisms [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 9 \| Group Homomorphisms		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 1 \| Introductions and Cauchy-Schwarz Inequality [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hilbert Spaces 1 \| Introductions and Cauchy-Schwarz Inequality		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 8 \| Integers Modulo m ⤳ Abelian Group [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 8 \| Integers Modulo m ⤳ Abelian Group		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 7 \| Abelian Groups [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 7 \| Abelian Groups		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 41 \| Measurable Sets and Null Sets [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 41 \| Measurable Sets and Null Sets		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 17 \| Picard–Lindelöf Theorem (General and Special Version) [dark]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 17 \| Picard–Lindelöf Theorem (General and Special Version)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 6 \| Cancellation Property [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 6 \| Cancellation Property		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 26 \| Proof of the Implicit Function Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 26 \| Proof of the Implicit Function Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 25 \| Implicit Function Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 25 \| Implicit Function Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 40 \| Integral Is Well-Defined [dark version]	流形 40 积分是良定义的 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 40 \| Integral Is Well-Defined		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 24 \| Application of the Inverse Function Theorem [dark version]	多元微积分 24 逆函数定理的应用 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮的一面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 24 \| Application of the Inverse Function Theorem	多变量微积分 24 反函数定理的应用	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 22 \| Local Diffeomorphisms [dark version]	多变量微积分 22 局部微分同胚 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 22 \| Local Diffeomorphisms	多变量微积分 22 局部微分同胚	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 12 \| Parseval's Identity for Step Functions [dark version]	傅里叶变换 12 阶跃函数的帕塞瓦尔恒等式 [暗色版本]	The Bright Side of Mathematics - Videos	数学的阳光面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 12 \| Parseval's Identity for Step Functions	傅里叶变换 12 针对阶跃函数的帕塞瓦尔恒等式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 11 \| Sum Formulas for Sine and Cosine [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 11 \| Sum Formulas for Sine and Cosine		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 24 \| Homomorphisms and Isomorphisms [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 24 \| Homomorphisms and Isomorphisms	抽象线性代数 24 同态与同构	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 10 \| Fundamental Example for Fourier Series [dark version]	傅里叶变换 10 傅里叶级数的基础示例 [暗色版本]	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 10 \| Fundamental Example for Fourier Series	傅里叶变换 10 傅里叶级数的基本示例	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 38 \| Integration for Differential Forms [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 38 \| Integration for Differential Forms	流形 38 微分形式的积分	The Bright Side of Mathematics - Videos	数学光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 23 \| Combinations of Linear Maps [dark version]	抽象线性代数 23 线性映射的组合 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 62 \| Recipe for Calculating Eigenvectors [dark version]	线性代数 62 计算特征向量的秘诀 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 62 \| Recipe for Calculating Eigenvectors	线性代数 62 计算特征向量的方法	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 23 \| Combinations of Linear Maps	抽象线性代数 23 线性映射的组合	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 22 \| Linear Maps [dark version]	抽象线性代数 22 线性映射 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 22 \| Linear Maps	抽象线性代数 22 线性映射	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 37 \| Unit Normal Vector Field [dark version]	流形 37 单位法向量场 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 37 \| Unit Normal Vector Field	流形 37 单位法向量场	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 8 \| Bessel's Inequality and Parseval's Identity [dark version]	傅里叶变换 8 贝塞尔不等式和帕塞瓦尔恒等式 [暗色版本]	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 8 \| Bessel's Inequality and Parseval's Identity	傅里叶变换 8 贝塞尔不等式和帕塞瓦尔恒等式	The Bright Side of Mathematics - Videos	数学的阳光面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 36 \| Examples for Volume Forms [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 36 \| Examples for Volume Forms	流形 36 体积形式的例子	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 16 \| Periodic Solutions and Fixed Points [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 16 \| Periodic Solutions and Fixed Points		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 7 \| Complex Fourier Series [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 7 \| Complex Fourier Series		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 6 \| Fourier Series in L² [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 6 \| Fourier Series in L²		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 21 \| Example for Gram-Schmidt Process [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 21 \| Example for Gram-Schmidt Process		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 20 \| Gram-Schmidt Orthonormalization [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 20 \| Gram-Schmidt Orthonormalization		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Banach Fixed-Point Theorem [dark version]	巴拿赫不动点定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的闪光面 - 视频	The Bright Side of Mathematics	原始链接
Banach Fixed-Point Theorem	巴拿赫不动点定理	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 5 \| Integrable Functions [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 5 \| Integrable Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
How to Learn with Problem Sheets (good and bad ones)	如何利用习题册（好的和差的）进行学习	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 19 \| Fourier Coefficients [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 19 \| Fourier Coefficients		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 3 \| Orthogonal Basis [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 3 \| Orthogonal Basis		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 18 \| Orthonormal Basis [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 18 \| Orthonormal Basis		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Weierstrass M-Test [dark version]	外尔斯特拉斯M判别法 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Unbounded Operators 8 \| Adjoint Operators [dark version]	无界算子 8 伴随算子 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Unbounded Operators 8 \| Adjoint Operators	无界算子 8 伴随算子	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Weierstrass M-Test	外尔施特拉斯M判别法	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 24 \| Markov Chains [dark version]	概率论 24 马尔可夫链 [黑暗版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 24 \| Markov Chains		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 17 \| Approximation Formula [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 17 \| Approximation Formula	抽象线性代数 17 近似公式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 4 \| Quotient Spaces [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 16 \| Gramian Matrix [dark version]	抽象线性代数十六格拉姆矩阵 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 16 \| Gramian Matrix	抽象线性代数 16 格拉姆矩阵	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 15 \| Orthogonal Projection Onto Subspace [dark version]	抽象线性代数 15 正交投影到子空间上 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 15 \| Orthogonal Projection Onto Subspace	抽象线性代数 15 到子空间上的正交投影	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 15 \| Phase Portrait [dark version]	常微分方程 15 相图 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 14 \| Orthogonal Projection Onto Line [dark version]	抽象线性代数 14 正交投影到直线上 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 14 \| Orthogonal Projection Onto Line	抽象线性代数 14 正交投影到直线	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 15 \| Phase Portrait	常微分方程 15 相轨图	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 13 \| Orthogonality [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 13 \| Orthogonality		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 34 \| Examples for Riemannian Manifolds [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 34 \| Examples for Riemannian Manifolds		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 33 \| Riemannian Metrics [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 33 \| Riemannian Metrics		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Update April 2024 - A Big Thank You!	更新 2024年4月 - 非常感谢！	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 32 \| Alternative Definitions for Orientations [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 32 \| Alternative Definitions for Orientations		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 21 \| Diffeomorphisms [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 21 \| Diffeomorphisms		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 31 \| Orientable Manifolds [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 31 \| Orientable Manifolds		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 2 \| Trigonometric Polynomials [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 2 \| Trigonometric Polynomials		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 1 \| Introduction [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 4 \| Groups [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 4 \| Groups		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Fourier Transform 1 \| Introduction		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 12 \| Cauchy-Schwarz Inequality [dark version]	抽象线性代数 12 柯西-施瓦茨不等式 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 12 \| Cauchy-Schwarz Inequality	抽象线性代数 12 柯西-施瓦茨不等式	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 13 \| Picard Iteration [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 13 \| Picard Iteration		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 30 \| Examples of Differential Forms [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 30 \| Examples of Differential Forms		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 12 \| Picard–Lindelöf Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 12 \| Picard–Lindelöf Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 11 \| Banach Fixed Point Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 11 \| Banach Fixed Point Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 10 \| Inner Products [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 10 \| Inner Products		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex numbers: Solving Equations (with example) [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 29 \| Differential Forms [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 29 \| Differential Forms		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Reals 4 \| Construction [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Reals 2 \| Completeness Axiom [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Reals 1 \| Cauchy Sequences [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Unbounded Operators 7 \| Graph Norm and Closed Operators [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Unbounded Operators 7 \| Graph Norm and Closed Operators		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 33 \| Spectrum of Compact Operators [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 32 \| Normal and Self-Adjoint Operators [dark version]	泛函分析 32 正规算子和自伴算子 [深色版本]	The Bright Side of Mathematics - Videos	数学的美好一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 31 \| Spectral Radius [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Unbounded Operators 6 \| Closed Graph Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Unbounded Operators 6 \| Closed Graph Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Calculating the kernel of a matrix - An example [dark version]	计算矩阵的核 - 示例 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
QR decomposition (for square matrices) [dark version]	QR分解（针对方阵）[暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 23 \| Stochastic Processes		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 23 \| Stochastic Processes [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Complex Numbers 3 \| Absolute Value, Conjugate, Argument [dark version]	开始学习复数 3 绝对值、共轭、幅角 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Complex Numbers 1 \| Introduction [dark version]	开始学习复数 1 介绍 [暗色版本]	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 64 \| Cauchy Principal Value [dark version]	实分析 64 柯西主值 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 9 \| Example for Change of Basis [dark version]	抽象线性代数 9 基变换示例 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 9 \| Example for Change of Basis	抽象线性代数 9 基变换例子	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 62 \| Integral Test for Series [dark version]	实分析 62 级数积分判别法 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 8 \| Transformation Matrix [dark version]	抽象线性代数 8 变换矩阵 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 8 \| Transformation Matrix		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 8 \| Bayes's Theorem and Total Probability [dark version]	概率论 8 贝叶斯定理和全概率 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 8 \| Bayes's Theorem and Total Probability	概率论 8 贝叶斯定理和全概率	The Bright Side of Mathematics - Videos	数学的乐趣 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 61 \| Comparison Test for Integrals [dark version]	实分析 61 积分比较判别法 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 60 \| Integrals on Unbounded Domains [dark version]	实变函数 60 无界区域上的积分 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 28 \| Wedge Product [dark version]	流形 28 楔积 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 28 \| Wedge Product	流形 28 楔积	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 59 \| Integration by Partial Fraction Decomposition [dark version]	实分析 59 部分分式分解积分法 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 58 \| Integration by Parts [dark version]	实分析 58 分部积分 [暗色版本]	The Bright Side of Mathematics - Videos	数学的阳光面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 13 \| Convolution [dark version]	分布 13 卷积 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 13 \| Convolution		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 7 \| Change of Basis [dark version]	抽象线性代数 7 基变换 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 7 \| Change of Basis	抽象线性代数 7 基变换	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
A Table You Should Remember (Sine and Cosine) [dark version]	记住这个表格（正弦和余弦）[深色版本]	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 56 \| Proof of the Fundamental Theorem of Calculus [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 2 \| Semigroups [dark version]	代数2 半群 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Update for 2024 - Search and Quizzes	2024 年更新 - 搜索和测验	The Bright Side of Mathematics - Videos	数学的明亮一面 — 视频	The Bright Side of Mathematics	原始链接
Algebra 2 \| Semigroups	代数2 半群	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 55 \| Second Fundamental Theorem of Calculus [dark version]	实分析 55 微积分第二基本定理 [黑暗版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 6 \| Example of Basis Isomorphism [dark version]	抽象线性代数 6 基底同构的例子 [黑暗版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 6 \| Example of Basis Isomorphism	抽象线性代数 6 基同构的例子	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 54 \| First Fundamental Theorem of Calculus [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Unbounded Operators 5 \| Example [dark version]	无界算子 5 示例 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Unbounded Operators 5 \| Example	无界算子 5 示例	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 53 \| Riemann Integral - Properties [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 1 \| Introduction [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Algebra 1 \| Introduction	代数 1 引言	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 52 \| Riemann Integral - Examples [dark version]	实分析 52 黎曼积分 - 例子 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 27 \| Alternating k-forms [dark version]	流形 27 交错 k-形式 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 27 \| Alternating k-forms	流形 27 交替k-形式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 50 \| Properties of the Riemann Integral for Step Functions [dark version]	实分析 50 黎曼积分对于阶跃函数的性质 [暗黑版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 4 \| Basis, Linear Independence, Generating Sets [dark version]	抽象线性代数 4 基础、线性无关、生成集 [深色版本]	The Bright Side of Mathematics - Videos	数学的妙趣 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 4 \| Basis, Linear Independence, Generating Sets	抽象线性代数 4 基, 线性无关性, 生成集	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 48 \| Riemann Integral - Partitions [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 22 \| Conditional Expectation (given random variables) [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 22 \| Conditional Expectation (given random variables)	概率论 22 条件期望 (给定随机变量)	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 47 \| Proof of Taylor's Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 26 \| Ricci Calculus [dark version]	流形 26 里奇微积分 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 26 \| Ricci Calculus	流形 26 Ricci微积分	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 45 \| Taylor's Theorem [dark version]	实分析 45 泰勒定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 44 \| Higher Derivatives [dark version]	实分析 44 高阶导数 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 21 \| Conditional Expectation (given events) [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 21 \| Conditional Expectation (given events)	概率论 21 条件期望 (给定事件)	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 43 \| Other L'Hospital's Rules [dark version]	实分析 43 其他洛必达法则 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Unbounded Operators 3 \| Closed Operators [dark version]	无界算子 3 闭算子 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Unbounded Operators 3 \| Closed Operators	无界算子 3 闭算子	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 42 \| L'Hospital's Rule [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 41 \| Mean Value Theorem [dark version]	实分析 41 中值定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 2 \| Examples of Abstract Vector Spaces [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 2 \| Examples of Abstract Vector Spaces	抽象线性代数 2 抽象向量空间的例子	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 39 \| Derivatives of Inverse Functions [dark version]	实分析 39 反函数的导数 [黑暗版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 24 \| Differential in Local Charts [dark version]	流形 24 在局部图下的微分 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 24 \| Differential in Local Charts		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 38 \| Examples of Derivatives and Power Series [dark version]	实分析 38 导数和幂级数示例 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 37 \| Uniform Convergence for Differentiable Functions [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 36 \| Chain Rule [dark version]	实分析 36 链式法则 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
How to Use My Videos to Start Learning Mathematics	如何使用我的视频开始学习数学	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 12 \| Finite-Order Distributions [dark version]	分布 12 有限阶分布 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 12 \| Finite-Order Distributions	分布 12 有限阶分布	The Bright Side of Mathematics - Videos	数学的美好一面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 1 \| Vector Space [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 1 \| Vector Space	抽象线性代数 1 向量空间	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Learn Linear Algebra with my Videos	通过我的视频学习线性代数	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 65 \| Diagonalizable Matrices [dark version]	线性代数 65 可对角化的矩阵 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 65 \| Diagonalizable Matrices	线性代数 65 可对角化矩阵	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 34 \| Differentiability [dark version]	实分析 34 可微性 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Learn with the Map of Mathematics (and with my videos)	使用数学地图学习 (以及我的视频)	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 33 \| Some Continuous Functions [dark version]	实分析 33 一些连续函数 [深色版本]	The Bright Side of Mathematics - Videos	数学的美好的一面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 23 \| Differential (Definition) [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 23 \| Differential (Definition)	流形 23 微分 (定义)	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 32 \| Intermediate Value Theorem [dark version]	实分析 32 中值定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 63 \| Spectral Mapping Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 63 \| Spectral Mapping Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 31 \| Uniform Limits of Continuous Functions are Continuous [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Jordan Normal Form 2 \| An Example [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Unbounded Operators 1 \| Introduction and Definitions [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Unbounded Operators 1 \| Introduction and Definitions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 29 \| Spectrum of Multiplication Operator [dark version]	泛函分析 29 乘法算子的谱 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 28 \| Spectrum of Bounded Operators [dark version]	泛函分析 28 有界算子的谱 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 22 \| Coordinate Basis [dark version]	流形 22 坐标基 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 26 \| Open Mapping Theorem [dark version]	泛函分析 26 开映射定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 22 \| Coordinate Basis	流形 22 坐标基	The Bright Side of Mathematics - Videos	数学的明亮的一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 25 \| Hahn–Banach Theorem [dark version]	泛函分析 25 哈恩-巴拿赫定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 24 \| Uniform Boundedness Principle / Banach–Steinhaus Theorem [dark version]	泛函分析 24 一致有界性原理巴拿赫–施坦豪斯定理 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 61 \| Similar Matrices [dark version]	线性代数 61 相似矩阵 [暗色版本]	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis Live - Problem Solving - Derivatives	实分析直播 - 解题 - 导数	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 23 \| Dual Space - Example [dark version]	泛函分析 23 对偶空间 - 示例 [深色版本]	The Bright Side of Mathematics - Videos	数学的阳光面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 61 \| Similar Matrices	线性代数 61 相似矩阵	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 21 \| Isomorphisms [dark version]	泛函分析 21 同构 [暗色版]	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Jordan Normal Form 1 \| Overview [dark version]	约旦标准型 1 概述 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 20 \| Minkowski Inequality [dark version]	泛函分析 20 Minkowski 不等式 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 60 \| Selfadjoint and Unitary Matrices [dark version]	线性代数 60 自伴和酉矩阵 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 60 \| Selfadjoint and Unitary Matrices	线性代数 60 自伴和酉矩阵	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 19 \| Hölder's Inequality [dark version]	泛函分析 19 Hölder 不等式 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 18 \| Compact Operators [dark version]	泛函分析 18 紧算子 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 59 \| Adjoint [dark version]	线性代数 59 伴随 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 59 \| Adjoint	线性代数 59 伴随	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 16 \| Compact Sets [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 9 \| Lipschitz Continuity [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 9 \| Lipschitz Continuity	常微分方程 9 利普希茨连续性	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 15 \| Riesz Representation Theorem [dark version]	泛函分析 15 Riesz表示定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 14 \| Example Operator Norm [dark version]	泛函分析 14 示例算子范数 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 21 \| Tangent Space (Definition via tangent curves) [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 21 \| Tangent Space (Definition via tangent curves)	流形 21 切空间 (通过切曲线的定义)	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 58 \| Complex Vectors and Complex Matrices [dark version]	线性代数 58 复向量和复矩阵 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 58 \| Complex Vectors and Complex Matrices	线性代数 58 复向量和复矩阵	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 12 \| Continuity [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 11 \| Orthogonality [dark version]	函数分析 11 正交性 [暗色版本]	The Bright Side of Mathematics - Videos	数学的阳光一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 10 \| Cauchy-Schwarz Inequality [dark version]	泛函分析 10 柯西-施瓦茨不等式 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 57 \| Spectrum of Triangular Matrices [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 57 \| Spectrum of Triangular Matrices	线性代数57 三角矩阵的谱	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 9 \| Examples of Inner Products and Hilbert Spaces [dark version]	功能分析9 内积与希尔伯特空间实例 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 8 \| Existence and Uniqueness? [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 8 \| Existence and Uniqueness?	常微分方程 8 存在与唯一性	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 7 \| Examples of Banach Spaces [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 6 \| Norms and Banach Spaces [dark version]	功能分析6：范数与巴拿赫空间【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 34 \| Residue theorem [dark version]	复分析34 留数定理【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 55 \| Algebraic Multiplicity [dark version]	线性代数55 代数重数 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 55 \| Algebraic Multiplicity	线性代数 55 代数重数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 33 \| Residue for Poles [dark version]	复分析 33 极点的留数 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 31 \| Application of the Identity Theorem [dark version]	复分析 31 同一定理的应用 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Calculating Dimension and Basis of Range and Kernel [dark version]	计算像空间和核空间的维数和基 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 54 \| Characteristic Polynomial [dark version]	线性代数 54 特征多项式 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 54 \| Characteristic Polynomial	线性代数 54 特征多项式	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 30 \| Identity Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 29 \| Liouville's Theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 19 \| Tangent Space for Submanifolds [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 19 \| Tangent Space for Submanifolds	流形 19 子流形的切空间	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 28 \| Holomorphic Functions are C-infinity Functions [dark version]	复分析 28 全纯函数是 C-无穷函数 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 53 \| Eigenvalues and Eigenvectors [dark version]	线性代数 53 特征值与特征向量 [深色版本]	The Bright Side of Mathematics - Videos	数学的美妙之处 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 53 \| Eigenvalues and Eigenvectors	线性代数 53 特征值和特征向量	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 27 \| Cauchy's Integral Formula [dark version]	复分析 27 柯西积分公式 [暗黑版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 26 \| Keyhole contour [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 19 \| Covariance and Correlation [OLD dark version]	概率论19 协方差与相关性[旧版深色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 19 \| Covariance and Correlation [old version]	概率论19 协方差与相关性[旧版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 24 \| Winding Number [dark version]	复分析24 环绕数【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 23 \| Cauchy's theorem [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 52 \| Cramer's Rule [dark version]	线性代数 52 克莱姆法则 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 52 \| Cramer's Rule	线性代数52 克莱姆法则	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 5 \| Solve First-Order Autonomous Equations [dark version]	常微分方程5 解一阶自治方程 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 5 \| Solve First-Order Autonomous Equations		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 6 \| Separation of Variables [dark version]	常微分方程6 变量分离法 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 22 \| Goursat's Theorem [dark version]	复分析22 古尔萨定理 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 6 \| Separation of Variables	常微分方程6 变量分离法	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 3 \| Open and Closed Sets [dark version]	功能分析3 开集与闭集 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 21 \| Closed curves and antiderivatives [dark version]	复分析21 闭合曲线与反导数【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 51 \| Determinant for Linear Maps [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 51 \| Determinant for Linear Maps	线性代数51 线性映射的行列式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 20 \| Antiderivatives [dark version]	复分析20 原函数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 50 \| Gaussian Elimination for Determinants [dark version]	线性代数50 行列式的高斯消元法【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 50 \| Gaussian Elimination for Determinants	线性代数50 行列式的高斯消元法	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 18 \| Complex Contour Integral [dark version]	复分析18 复变函数积分【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 17 \| Complex Integration on Real Intervals [dark version]	复分析 17 实区间上的复积分 [暗色版本]	The Bright Side of Mathematics - Videos	数学的阳光一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 48 \| Laplace Expansion [dark version]	线性代数 48 拉普拉斯展开 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 48 \| Laplace Expansion	线性代数 48 拉普拉斯展开	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 20 \| Sylvester's Criterion [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 20 \| Sylvester's Criterion	多元微积分 20 西尔维斯特判据	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 15 \| Laurent Series [dark version]	复变函数 15 洛朗级数 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 14 \| Powers [dark version]	复分析 14 幂 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 47 \| Rule of Sarrus [dark version]	线性代数 47 萨吕规则 [暗色版本]	The Bright Side of Mathematics - Videos	数学的阳光面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 47 \| Rule of Sarrus		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 13 \| Complex Logarithm [dark version]	复分析 13 复对数 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 4 \| Reducing to First Order [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 4 \| Reducing to First Order	常微分方程 4 降为一阶	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 12 \| Exp, Cos and Sin as Power Series [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 46 \| Leibniz Formula for Determinants [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 46 \| Leibniz Formula for Determinants	线性代数 46 行列式的莱布尼茨公式	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 11 \| Power Series Are Holomorphic - Proof [dark version]	复分析 11 - 幂级数是全纯的 - 证明 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 19 \| Examples for Local Extrema [dark version]	多变量微积分 19 局部极值的例子 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 19 \| Examples for Local Extrema	多变量微积分 19个局部极值例子	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 9 \| Power Series [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 44 \| Determinant in 2 Dimensions [dark version]	线性代数 44 二维行列式 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 44 \| Determinant in 2 Dimensions	线性代数 44 二维行列式	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 8 \| Wirtinger Derivatives [dark version]	复分析 8 Wirtinger 导数 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 7 \| Cauchy-Riemann Equations Examples [dark version]	复变函数 7 柯西-黎曼方程示例 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 43 \| Determinant (Overview) [dark version]	线性代数 43 行列式 (概述) [黑暗版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 43 \| Determinant (Overview)	线性代数 43 行列式 (概述)	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 11 \| Rational Numbers (Ordering) [dark version]	开始学习数字 11 有理数 (排序) [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 10 \| Rational Numbers (Addition and Multiplication) [dark version]	开始学习单元 10 有理数 (加法和乘法) [暗色版]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 42 \| Uniqueness of Solutions [dark version]	线性代数 42 解的唯一性 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 42 \| Uniqueness of Solutions	线性代数 42 解的唯一性	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 9 \| Rational Numbers (Construction) [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Numbers 8 \| Integers (Multiplication) [dark version]	开始学习数字 8 整数 (乘法) [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
PLU decomposition - An Example [dark version]	PLU分解 - 一个例子 [暗色版本]	The Bright Side of Mathematics - Videos	数学的亮点 - 视频	The Bright Side of Mathematics	原始链接
Baire Category Theorem [dark version]	Baire 纲定理 [黑暗版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 6 \| Cauchy-Riemann Equations [dark version]	复分析 6 柯西-黎曼方程 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 40 \| Row Echelon Form [dark version]	线性代数 40 行阶梯形 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 40 \| Row Echelon Form	线性代数 40 行阶梯形	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 22 \| Outer measures - Part 3: Proof [dark version]	测度论 22 外测度 - 第三部分证明 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 21 \| Outer measures - Part 2: Examples [dark version]	测度论 21 外测度 - 第2部分例子 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 39 \| Gaussian Elimination [dark version]	线性代数 39 高斯消元 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
How NOT to Learn Mathematics	如何不学习数学	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 39 \| Gaussian Elimination	线代 39 高斯消元法	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 20 \| Outer measures - Part 1 [dark version]	测度论 20 外测度 - 第1部分 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 19 \| Fubini's Theorem [dark version]	测度论 19 富比尼定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 38 \| Set of Solutions [dark version]	线性代数 38 解集 [暗色版本]	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 38 \| Set of Solutions	线性代数 38 解集	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Baire Category Theorem	Baire范畴定理	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 7 \| Integers (Addition and Inverses) [dark version]	开始学习数字 7 整数 (加法和逆元) [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 18 \| Local Extrema [dark version]	多元微积分 18 局部极值 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 18 \| Local Extrema	多变量微积分 18 局部极值	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 17 \| Product measure and Cavalieri's principle [dark version]	测度论 17 乘积测度与卡瓦列里原理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 16 \| Proof of the Substitution Rule for Measure Spaces [dark version]	测度论 16 测度空间换元法则的证明 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 2 \| Definitions [dark version]	常微分方程 2 定义 [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 2 \| Definitions	常微分方程 2 定义	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 14 \| Radon-Nikodym theorem and Lebesgue's decomposition theorem [dark version]	测度论 14 Radon-Nikodym 定理和勒贝格分解定理 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 13 \| Lebesgue-Stieltjes Measures [dark version]	测度论 13 Lebesgue-Stieltjes 测度 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 12 \| Carathéodory's Extension Theorem [dark version]	测度论 12 卡拉西奥多里扩张定理 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 37 \| Row Operations [dark version]	线性代数 37 行运算 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 37 \| Row Operations	线性代数 37 行运算	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 5 \| Natural Numbers (Multiplication) [dark version]	开始学习数字 5 自然数 (乘法) [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 4 \| Natural Numbers (Ordering) [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 1 \| Introduction [dark version]	常微分方程 1 引言 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 1 \| Introduction	常微分方程 1 导论	The Bright Side of Mathematics - Videos	数学的阳光面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 2 \| Natural Numbers (Successor Map and Addition) [dark version]	开始学习数字 2 自然数 (后继映射与加法) [深色版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 1 \| Natural Numbers (in Set Theory) [dark version]	开始学习数字 1 自然数 (在集合论中) [深色版本]	The Bright Side of Mathematics - Videos	数学的乐趣 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Sets 7 \| Composition of Maps [dark version]	开始学习集合7 映射的构成【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Sets 6 \| Injectivity, Surjectivity and Bijectivity [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 9 \| Coordinate Transformation [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 8 \| Multiplication with Smooth Functions [dark version]	分布8 与光滑函数的乘法【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 6 \| The Delta Distribution Is Not Regular [dark version]	分布6 德尔塔分布非正则版【暗黑风格】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 5 \| Regular Distributions [dark version]	分布 5 常规分布 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis Live - Problem Solving - Differentiable Functions	实分析直播 - 解题篇 - 可微函数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 2 \| Test Functions [dark version]	分布 2 检验函数 [深色版本]	The Bright Side of Mathematics - Videos	数学光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Sets 5 \| Range, Image and Preimage [dark version]	开始学习集合5 值域、像和原像 [深色版本]	The Bright Side of Mathematics - Videos	数学的阳光一面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Sets 4 \| Cartesian Product and Maps [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis Live - Problem Solving - Continuous Functions	实分析直播 - 解题 - 连续函数	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 35 \| Rank-Nullity Theorem [dark version]	线性代数 35 秩-零化度定理 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis Live - Problem Solving - Series and Convergent Criteria	实分析直播 - 解题系列与收敛准则	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 35 \| Rank-Nullity Theorem	线性代数 35 秩-零化度定理	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 34 \| Range and Kernel of a Matrix [dark version]	线性代数34 矩阵的值域与核空间 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 34 \| Range and Kernel of a Matrix	线性代数 34 矩阵的值域和核	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 18 \| Regular Value Theorem (abstract version) [dark version]	流形 18 正则值定理（抽象版）[暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 18 \| Regular Value Theorem (abstract version)	流形 18 正则值定理（抽象版）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 17 \| Examples of Smooth Maps [dark version]	流形17 光滑映射示例【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 16 \| Smooth Maps (Definition) [dark version]	流形16 光滑映射（定义）[暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
A Bright Channel Update - 2023	2023年光明频道更新	The Bright Side of Mathematics - Videos	数学之光——视频集锦	The Bright Side of Mathematics	原始链接
Manifolds 14 \| Submanifolds [dark version]	流形14 子流形 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 13 \| Examples of Smooth Manifolds [dark version]	流形13 光滑流形示例【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 12 \| Smooth Structures [dark version]	流形12 光滑结构【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 10 \| Distributional Derivative [dark version]	分布 10 分布导数 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 10 \| Distributional Derivative	分布 10 分布导数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 11 \| Projective Space is a Manifold [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 9 \| Locally Euclidean Spaces [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Sets 2 \| Predicates, Equality and Subsets [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 33 \| Transpose and Inner Product [dark version]	线性代数33 转置与内积 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 33 \| Transpose and Inner Product	线性代数33 转置与内积	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 7 \| Continuity [dark version]	流形7 连续性 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 6 \| Second-Countable Space [dark version]	流形6 第二可数空间【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 30 \| Continuous Images of Compact Sets are Compact [dark version]	实分析30 紧集的连续像也是紧集【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 29 \| Combination of Continuous Functions [dark version]	实分析29 连续函数的组合 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 32 \| Transposition for Matrices [dark version]	线性代数32 矩阵的转置 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 32 \| Transposition for Matrices	线性代数32 矩阵的转置	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 5 \| Projective Space [dark version]	流形5 射影空间【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Sets 1 \| Overview and Element Relation [dark version]	开始学习集合1：概述与元素关系【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 31 \| Inverses of Linear Maps are Linear [dark version]	线性代数31 线性映射的逆也是线性的[暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 31 \| Inverses of Linear Maps are Linear		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 27 \| Continuity and Examples [dark version]	实分析27 连续性与示例 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 26 \| Limits of Functions [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 29 \| Identity and Inverses [dark version]	线性代数29 单位矩阵与逆矩阵 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 28 \| Conservation of Dimension [dark version]	线性代数28 维数守恒【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 25 \| Uniform Convergence [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 27 \| Dimension of a Subspace [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 26 \| Steinitz Exchange Lemma [dark version]	线性代数26 斯泰尼茨交换引理 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 25 \| Coordinates with respect to a Basis [dark version]	线性代数25 基下的坐标【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 24 \| Pointwise Convergence [dark version]	实分析24 逐点收敛 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 23 \| Sequence of Functions [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 23 \| Linear Independence (Examples) [dark version]	线性代数23 线性无关性（示例）[暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 22 \| Linear Independence (Definition) [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 21 \| Examples of Linear Maps [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 20 \| Linear maps induce matrices [dark version]	线性代数20 线性映射诱导矩阵【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 19 \| Matrices induce linear maps [dark version]	线性代数19 矩阵诱导线性映射【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 17 \| Properties of the Matrix Product [dark version]	线性代数17 矩阵乘积的性质 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 21 \| Reordering for Series [dark version]	实分析21 级数重排 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 11 \| Proof of Lebesgue's Dominated Convergence Theorem [dark version]	测度论11 勒贝格控制收敛定理的证明【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 20 \| Ratio and Root Test [dark version]	实分析20 比率与根检验 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 19 \| Comparison Test [dark version]	实分析19 比较判别法 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 18 \| Leibniz Criterion [dark version]	实分析18 莱布尼茨判别法 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 15 \| Series - Introduction [dark version]	实分析15 级数 - 引言 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 14 \| Heine-Borel Theorem [dark version]	实分析14 海涅-博雷尔定理 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 13 \| Open, Closed and Compact Sets [dark version]	实分析13 开集、闭集与紧集【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 12 \| Examples for Limit Superior and Limit Inferior [dark version]	实分析12 上极限与下极限的例子 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 11 \| Limit Superior and Limit Inferior [dark version]	实分析11 上极限与下极限 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 9 \| Subsequences and Accumulation Values [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 8 \| Example Calculation [dark version]	实分析8 示例计算 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 16 \| Matrix Product [dark version]	线性代数16 矩阵乘积 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 7 \| Cauchy Sequences and Completeness [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 15 \| Row Picture [dark version]	线性代数15 行图像 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 6 \| Supremum and Infimum [dark version]	实分析6 上确界与下确界 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 14 \| Column Picture of the Matrix-Vector Product [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 5 \| Sandwich Theorem [dark version]	实分析5 夹逼定理 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 13 \| Special Matrices [dark version]	线性代数13 特殊矩阵【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 11 \| Matrices [dark version]	线性代数11 矩阵【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 10 \| Cross Product [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 9 \| Inner Product and Norm [dark version]	线性代数9 内积与范数 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 7 \| Examples for Subspaces [dark version]	线性代数7 子空间示例【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 6 \| Linear Subspaces [dark version]	线性代数6 线性子空间 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 5 \| Vector Space ℝn [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 4 \| Lines in ℝ² [dark version]	线性代数4 ℝ²中的直线【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 2 \| Vectors in ℝ² [dark version]	线性代数2 ℝ²中的向量 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 1 \| Introduction [dark version]	线性代数1 引言 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 18 \| Properties of Variance and Standard Deviation [dark version]	概率论18 方差与标准差的性质【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Logic 2 \| Disjunction, Tautology and Logical Equivalence [dark version]	开始学习逻辑2：析取、重言式与逻辑等价 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Pauli matrices [dark version]	泡利矩阵 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Logic - Part 1 - Logical Statements, Negation and Conjunction [dark version]	开始学习逻辑 - 第一部分 - 逻辑陈述、否定与合取 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Restriction [dark version]	限制 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Sum Symbol [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Product Symbol [dark version]	产品标志 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Composition [dark version]	构图 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Gamma Function [dark version]	伽玛函数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Factorial [dark version]	阶乘 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Nabla-symbol [dark version]	Nabla符号[暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 17 \| Standard Deviation [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Levi-Civita Symbol [dark version]	列维-奇维塔符号 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Kronecker Delta [dark version]	克罗内克δ函数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 16 \| Variance [dark version]	概率论16 方差 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 14 \| Expectation and Change-of-Variables [dark version]	概率论14 期望与变量变换【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频集	The Bright Side of Mathematics	原始链接
Probability Theory 13 \| Independence for Random Variables [dark version]	概率论13 随机变量的独立性【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 12 \| Cumulative Distribution Function [dark version]	概率论 12 累积分布函数 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 10 \| Random Variables [dark version]	概率论10 随机变量【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 16 \| Taylor's Theorem [dark version]	多元微积分16 泰勒定理 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 16 \| Taylor's Theorem	多元微积分16 泰勒定理	The Bright Side of Mathematics - Videos	数学的光明面 - 视频集	The Bright Side of Mathematics	原始链接
Multivariable Calculus 14 \| Vector Fields and Potential Functions [dark version]	多元微积分14 向量场与势函数 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 13 \| Schwarz's Theorem [dark version]	多元微积分13 施瓦茨定理 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 12 \| Second Order Partial Derivatives [dark version]	多元微积分12 二阶偏导数 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 10 \| Directional Derivative [dark version]	多元微积分10：方向导数【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 9 \| Geometric Picture for the Gradient [dark version]	多元微积分9 梯度的几何图解【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 8 \| Gradient [dark version]	多元微积分8 梯度【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 7 \| Chain, Sum and Factor rule [dark version]	多元微积分7 链式法则、求和法则与乘积法则 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 5 \| Total Derivative [dark version]	多元微积分5 全导数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 4 \| Partial Derivatives [dark version]	多元微积分4：偏导数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 2 \| Continuity [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Infinity [dark version]	无限 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Quaternions [dark version]	四元数【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 9 \| Independence for Events [dark version]	概率论 9 事件的独立性 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Heaviside Function [dark version]	海维赛德函数【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Convolution [dark version]	卷积 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 1 \| Introduction [dark version]	多元微积分1 导论 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Laplace Operator [dark version]	拉普拉斯算子【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Mathematics - Introduction to the Course [dark version]	开始学习数学 - 课程简介 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Euler's Phi Function [dark version]	欧拉φ函数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Outer Product [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Little o [dark version]	小o [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 6 \| Hypergeometric Distribution [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 15 \| Multi-Index Notation [dark version]	多元微积分15 多重指标记号 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Multivariable Calculus 15 \| Multi-Index Notation	多元微积分15 多重指标记号	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Map Arrows [dark version]	地图箭头 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Beta Function [dark version]	Beta函数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 1 \| Motivation and Delta Function [dark version]	分布1：动机与Delta函数【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Modulo [dark version]	模 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 5 \| Product Probability Spaces [dark version]	概率论5 乘积概率空间 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Binomial Coefficient [dark version]	二项式系数 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 4 \| Binomial Distribution [dark version]	概率论4 二项分布 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Riemann integral vs. Lebesgue integral [dark version]	黎曼积分 vs. 勒贝格积分 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Big O [dark version]	大O符号【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Set Brackets [dark version]	设置支架 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Integers [dark version]	整数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Greek Letters in Mathematics [dark version]	数学中的希腊字母 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Integers	整数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 2 \| Interior, Exterior, Boundary, Closure [dark version]	流形2 内部、外部、边界、闭包 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 9 \| Fatou's Lemma [dark version]	测度论9 法图引理 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 2 \| Probability Measures [dark version]	概率论2 概率测度【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Natural Numbers [dark version]	自然数 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Natural Numbers	自然数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 3 \| Complex Derivative and Examples [dark version]	复变分析3 复导数与实例 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Closed Line Integral [dark version]	闭合线积分 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 1 \| Introduction and Topology [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 7 \| Monotone Convergence Theorem (and more) [dark version]	测度论7 单调收敛定理（及其他）[暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Closed Line Integral	闭路线积分	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 1 \| Introduction (including R) [dark version]	概率论1 引言（含R语言）[暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频集	The Bright Side of Mathematics	原始链接
Integral Symbol [dark version]	积分符号 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Integral Symbol		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 2 \| Examples for Metrics - Euclidean or Discrete Metric? [dark version]	功能分析2 度量示例——欧几里得或离散度量【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 6 \| Lebesgue Integral [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Inner Product [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 2 \| Complex Differentiability [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Inner Product	内积	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 1 \| Introduction [dark version]	复分析1 引言 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
D'Alembert Operator [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
D'Alembert Operator	达朗贝尔算符	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Partial d [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Partial d	部分	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 3 \| What is a measure? [dark version]	测度论3 什么是测度【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Subset Symbol [dark version]	子集符号 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Subset Symbol		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Empty Set [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Empty Set	空集	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 2 \| Borel Sigma Algebras [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Element Symbol [dark version]	元素符号 [深色版本]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
LU decomposition - An Example Calculation [dark version]	LU分解 - 计算示例 [暗色版本]	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Element Symbol	元素符号	The Bright Side of Mathematics - Videos	数学的光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 2 \| Sequences and Limits [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 1 \| Sigma Algebras [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 1 \| Introduction [dark version]	实分析1 导论 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 1 \| Metric Space - How to Measure Distances? [dark version]		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 29 \| Identity and Inverses		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 17 \| Examples of Smooth Maps		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 28 \| Conservation of Dimension		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 14 \| Vector Fields and Potential Functions	多元微积分14：向量场与势函数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 27 \| Dimension of a Subspace	线性代数27 子空间的维度	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 18 \| Properties of Variance and Standard Deviation	概率论18 方差与标准差的性质	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 16 \| Smooth Maps (Definition)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 34 \| Residue theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 33 \| Residue for Poles	复分析33 极点的留数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 31 \| Application of the Identity Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 26 \| Steinitz Exchange Lemma		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 25 \| Coordinates with respect to a Basis		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 30 \| Identity Theorem	复分析30 恒等定理	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 17 \| Standard Deviation		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 29 \| Liouville's Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 23 \| Linear Independence (Examples)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 22 \| Linear Independence (Definition)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 21 \| Examples of Linear Maps		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 28 \| Holomorphic Functions are C-infinity Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 20 \| Linear maps induce matrices		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 27 \| Cauchy's Integral Formula		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 26 \| Keyhole contour		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 13 \| Schwarz's Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 19 \| Matrices induce linear maps		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 24 \| Winding Number		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 17 \| Properties of the Matrix Product		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 23 \| Cauchy's theorem	复分析23 柯西定理	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 16 \| Matrix Product		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 12 \| Second Order Partial Derivatives		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 22 \| Goursat's Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 15 \| Row Picture		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 21 \| Closed curves and antiderivatives		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 20 \| Antiderivatives		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 10 \| Directional Derivative		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 14 \| Column Picture of the Matrix-Vector Product		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 13 \| Special Matrices		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 9 \| Geometric Picture for the Gradient		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 11 \| Matrices	线性代数 11 矩阵	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 33 \| Spectrum of Compact Operators		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 8 \| Gradient		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 7 \| Chain, Sum and Factor rule		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 5 \| Total Derivative		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 10 \| Cross Product		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 4 \| Partial Derivatives		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 14 \| Submanifolds		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 16 \| Variance		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 2 \| Continuity		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Multivariable Calculus 1 \| Introduction	多元微积分1 引言	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 9 \| Inner Product and Norm	线性代数9 内积与范数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 13 \| Examples of Smooth Manifolds		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 7 \| Examples for Subspaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 6 \| Linear Subspaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 64 \| Cauchy Principal Value		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 14 \| Expectation and Change-of-Variables		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 62 \| Integral Test for Series		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 18 \| Complex Contour Integral	复分析18 复变函数积分	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 17 \| Complex Integration on Real Intervals		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 61 \| Comparison Test for Integrals		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 60 \| Integrals on Unbounded Domains		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 59 \| Integration by Partial Fraction Decomposition		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 9 \| Coordinate Transformation		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 15 \| Laurent Series	复分析15 洛朗级数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 8 \| Multiplication with Smooth Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 12 \| Smooth Structures		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 58 \| Integration by Parts		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 11 \| Projective Space is a Manifold		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 5 \| Vector Space ℝn	线性代数5 向量空间ℝⁿ	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 14 \| Powers		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 11 \| Power Series Are Holomorphic - Proof		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 56 \| Proof of the Fundamental Theorem of Calculus		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 9 \| Locally Euclidean Spaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 13 \| Complex Logarithm		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 4 \| Lines in ℝ²		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 7 \| Continuity	流形 7 连续性	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 55 \| Second Fundamental Theorem of Calculus		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 12 \| Exp, Cos and Sin as Power Series		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Linear Algebra 2 \| Vectors in ℝ²	线性代数2 ℝ²中的向量	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra 1 \| Introduction		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 6 \| Second-Countable Space	流形6 第二可数空间	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 5 \| Projective Space	流形5 射影空间	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 54 \| First Fundamental Theorem of Calculus		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 4 \| Quotient Spaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 53 \| Riemann Integral - Properties		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 2 \| Interior, Exterior, Boundary, Closure		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Manifolds 1 \| Introduction and Topology		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 9 \| Power Series		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 13 \| Independence for Random Variables		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 32 \| Normal and Self-Adjoint Operators		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 8 \| Wirtinger Derivatives	复分析8 维尔廷格导数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 52 \| Riemann Integral - Examples	实分析52 黎曼积分—示例	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex Analysis 7 \| Cauchy-Riemann Equations Examples		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 6 \| Cauchy-Riemann Equations		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 3 \| Complex Derivative and Examples		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 2 \| Complex Differentiability		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 50 \| Properties of the Riemann Integral for Step Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Complex Analysis 1 \| Introduction	复分析1 引言	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Infinity	无限	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Quaternions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Heaviside Function	赫维赛德函数	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Convolution	卷积	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Laplace Operator		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Euler's Phi Function	欧拉函数	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Outer Product	外积	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Little o		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Map Arrows	地图箭头	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Complex Numbers 3 \| Absolute Value, Conjugate, Argument	开始学习复数3：绝对值、共轭复数、幅角	The Bright Side of Mathematics - Videos	数学的光明面 - 视频集	The Bright Side of Mathematics	原始链接
Beta Function		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Modulo		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Binomial Coefficient	二项式系数	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Big O		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Set Brackets		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Pauli matrices		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Restriction		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Product Symbol		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Sum Symbol		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 48 \| Riemann Integral - Partitions	实分析48 黎曼积分——分割	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Composition	构成	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Gamma Function	伽马函数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Factorial	阶乘	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Nabla-symbol		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Levi-Civita Symbol	Levi-Civita 符号	The Bright Side of Mathematics - Videos	数学的精彩一面 - 视频	The Bright Side of Mathematics	原始链接
Kronecker Delta	克罗内克δ	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Greek Letters in Mathematics		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 47 \| Proof of Taylor's Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 12 \| Cumulative Distribution Function		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 45 \| Taylor's Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hörsaalübung 7 - Lineare Algebra - Jordan-Normalform, Singulärwertzerlegung und Ausgleichsrechnung	课堂练习 7 - 线性代数 - 约当标准型，奇异值分解和最小二乘法	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Hörsaalübung 6 - Lineare Algebra - PLR-Zerlegung, QR-Zerlegung, Schurzerlegung, Jordan-Normalform	讲座练习六 - 线性代数 - PLR 分解, QR 分解, Schur 分解, Jordan 标准形	The Bright Side of Mathematics - Videos	数学的阳光面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 44 \| Higher Derivatives		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hörsaalübung 4 - Lineare Algebra - Skalarprodukte, Gram-Schmidt, Darstellungsmatrizen, Linearität	讲座练习4 - 线性代数 - 标量积、格拉姆-施密特正交化、表示矩阵、线性性	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 43 \| Other L'Hospital's Rules		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Hörsaalübung 3 - Lineare Algebra - Basiswechsel, Dimension, Lineare Unabhängig, Koordinatenvektor	练习课3 - 线性代数 - 基变换、维度、线性无关性、坐标向量	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Hörsaalübung 2 - Lineare Algebra - Vielfachheiten, Diagonalisieren, Vektorräume, Unterräume	课堂练习2 - 线性代数 - 多重性、对角化、向量空间、子空间	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Hörsaalübung 1 - Lineare Algebra - Komplexe Zahlen, Gleichungssysteme, Eigenwerte, Eigenvektoren	讲座练习1 - 线性代数 - 复数、方程组、特征值、特征向量	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 22 \| Outer measures - Part 3: Proof		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 10 \| Random Variables		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 9 \| Independence for Events		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 42 \| L'Hospital's Rule		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 41 \| Mean Value Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 39 \| Derivatives of Inverse Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 6 \| Hypergeometric Distribution	概率论6 超几何分布	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 38 \| Examples of Derivatives and Power Series		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 37 \| Uniform Convergence for Differentiable Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 36 \| Chain Rule		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 5 \| Product Probability Spaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 4 \| Binomial Distribution		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 34 \| Differentiability		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 33 \| Some Continuous Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Probability Theory 2 \| Probability Measures	概率论2 概率测度	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Probability Theory 1 \| Introduction (including R)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 32 \| Intermediate Value Theorem	实分析32 中值定理	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 31 \| Uniform Limits of Continuous Functions are Continuous		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Explaining Mathematics with OBS	用OBS解释数学	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 30 \| Continuous Images of Compact Sets are Compact		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 29 \| Combination of Continuous Functions	实分析 29 连续函数的组合	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 31 \| Spectral Radius		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 6 \| The Delta Distribution Is Not Regular		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 27 \| Continuity and Examples		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 26 \| Limits of Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 25 \| Uniform Convergence		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 24 \| Pointwise Convergence		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 23 \| Sequence of Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 21 \| Reordering for Series		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 20 \| Ratio and Root Test		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 19 \| Comparison Test		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 18 \| Leibniz Criterion		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 15 \| Series - Introduction		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 14 \| Heine-Borel Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 13 \| Open, Closed and Compact Sets		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 12 \| Examples for Limit Superior and Limit Inferior		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 11 \| Limit Superior and Limit Inferior		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 9 \| Subsequences and Accumulation Values		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 8 \| Example Calculation		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 7 \| Cauchy Sequences and Completeness	实分析7 柯西序列与完备性	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 6 \| Supremum and Infimum	实分析6 上确界与下确界	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 5 \| Sandwich Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Real Analysis 2 \| Sequences and Limits	实分析2 序列与极限	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis 1 \| Introduction	实分析1 导论	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Complex Numbers 1 \| Introduction	开始学习复数 1 简介	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Reals 4 \| Construction		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 29 \| Spectrum of Multiplication Operator		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Reals 2 \| Completeness Axiom		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Reals 1 \| Cauchy Sequences	开始学习实数1 柯西序列	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 11 \| Rational Numbers (Ordering)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 28 \| Spectrum of Bounded Operators		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Numbers 10 \| Rational Numbers (Addition and Multiplication)	开始学习数字10 有理数（加法与乘法）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 9 \| Rational Numbers (Construction)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Numbers 8 \| Integers (Multiplication)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Numbers 7 \| Integers (Addition and Inverses)	开始学习数字7 整数（加法与逆运算）	The Bright Side of Mathematics - Videos	《数学的光明面》- 视频集	The Bright Side of Mathematics	原始链接
Start Learning Numbers 5 \| Natural Numbers (Multiplication)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Numbers 4 \| Natural Numbers (Ordering)	开始学习数字4 自然数（排序）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Numbers 2 \| Natural Numbers (Successor Map and Addition)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Numbers 1 \| Natural Numbers (in Set Theory)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Sets 7 \| Composition of Maps		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Sets 6 \| Injectivity, Surjectivity and Bijectivity	开始学习集合6：单射、满射与双射	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Lösungen - LR-Zerlegung, QR-Zerlegung, Darstellungsmatrix und Spektrum	解答 - LR分解, QR分解, 表示矩阵和谱	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Sets 5 \| Range, Image and Preimage		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Start Learning Sets 4 \| Cartesian Product and Maps	开始学习集合4：笛卡尔积与映射	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Sets 2 \| Predicates, Equality and Subsets		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Lösungen - Diagonalisierbare Matrizen und abstrakte Vektorräume	解答 - 可对角化矩阵和抽象向量空间	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Sets 1 \| Overview and Element Relation		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Lösungen - Eigenwerte, Eigenvektoren, hermitesche, unitäre und normale Matrizen	解答 - 特征值，特征向量，厄米特矩阵、酉矩阵和正规矩阵	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Logic 2 \| Disjunction, Tautology and Logical Equivalence		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Lösungen - Polarkoordinaten, Vektoren in Ebene und Determinanten	解答 - 极坐标、平面向量与行列式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频集	The Bright Side of Mathematics	原始链接
Start Learning Logic 1 \| Logical Statements, Negations and Conjunction	开始学习逻辑1：逻辑陈述、否定与合取	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Start Learning Mathematics - Introduction to the Course	开始学习数学 - 课程介绍	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 26 \| Open Mapping Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributions 5 \| Regular Distributions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 25 \| Hahn–Banach Theorem	泛函分析25 哈恩-巴拿赫定理	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 24 \| Uniform Boundedness Principle / Banach–Steinhaus Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 23 \| Dual Space - Example	功能分析23 对偶空间示例	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
A Table You Should Remember (Sine and Cosine)	应记住的表格 (正弦和余弦)	The Bright Side of Mathematics - Videos	数学的光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 21 \| Isomorphisms	《泛函分析21 同构关系》	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 20 \| Minkowski Inequality	泛函分析20 闵可夫斯基不等式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 19 \| Hölder's Inequality		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 18 \| Compact Operators		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 16 \| Compact Sets		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 15 \| Riesz Representation Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
PLU decomposition - An Example	PLU分解——一个示例	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 14 \| Example Operator Norm		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 12 \| Continuity		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 11 \| Orthogonality		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 10 \| Cauchy-Schwarz Inequality	泛函分析十柯西-施瓦茨不等式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 9 \| Examples of Inner Products and Hilbert Spaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 7 \| Examples of Banach Spaces	泛函分析7 巴拿赫空间的例子	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 6 \| Norms and Banach Spaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 3 \| Open and Closed Sets	《功能分析3：开集与闭集》	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Functional Analysis 2 \| Examples for Metrics - Euclidean or Discrete Metric?		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Functional Analysis 1 \| Metric Space - How to Measure Distances?	功能分析1 度量空间——如何测量距离	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Jordan Normal Form 2 \| An Example	Jordan标准形2 一个例子	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Jordan Normal Form 1 \| Overview	Jordan标准型 1 概述	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 21 \| Outer measures - Part 2: Examples		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Äußere Maße - Teil 2: Beispiele	外部尺寸 - 第二部分示例	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 20 \| Outer measures - Part 1		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Äußere Maße - Teil 1	外部尺寸 - 第一部分	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributionen - Teil 4: Raum der Distributionen		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributionen - Teil 3: Konvergenz von Testfunktionen	分布——第三部分测试函数的收敛性	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 2 \| Test Functions		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributionen - Teil 2: Testfunktionen	分布 - 第2部分测试函数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Distributions 1 \| Motivation and Delta Function		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Distributionen - Teil 1: Motivation und Delta-Funktion		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
QR decomposition (for square matrices)	QR分解（针对方阵）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 19 \| Fubini's Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Satz von Fubini	富比尼定理	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Prinzip von Cavalieri - Beispiel	卡瓦列里原理 - 示例	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 17 \| Product measure and Cavalieri's principle		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Produktmaß und Prinzip von Cavalieri	积测度和卡瓦列里原理	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 16 \| Proof of the Substitution Rule for Measure Spaces		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Substitutionsformel für Maßräume - Beweis	测度空间的替换公式 - 证明	The Bright Side of Mathematics - Videos	数学的璀璨面 - 视频	The Bright Side of Mathematics	原始链接
LU decomposition - An Example Calculation	LU分解—计算示例	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 14 \| Radon-Nikodym theorem and Lebesgue's decomposition theorem	测度论14 拉东-尼科迪姆定理与勒贝格分解定理	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Complex numbers: Solving Equations (with example)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Komplexe Zahlen: Gleichungen lösen - inklusive Beispielrechnung		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 13 \| Lebesgue-Stieltjes Measures		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Maßtheorie - Part 13 - Lebesgue-Stieltjes-Maße	测度论 - 第13部分 - Lebesgue-Stieltjes 测度	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 12 \| Carathéodory's Extension Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 11 \| Proof of Lebesgue's Dominated Convergence Theorem		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 9 \| Fatou's Lemma		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 7 \| Monotone Convergence Theorem (and more)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 6 \| Lebesgue Integral	测度论6 勒贝格积分	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 3 \| What is a measure?		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Calculating dimension and basis of range and kernel		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
The Bright Side of Mathematics - Channel Introduction		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Measure Theory 2 \| Borel Sigma Algebras	测度论2 Borel Sigma代数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Measure Theory 1 \| Sigma Algebras		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Determinanten - Teil1 - Determinante in 2 Dimensionen	行列式 - 第一部分 - 二维行列式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Determinanten - Ein Überblick		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Dimension und Basis von Bild und Kern einer Matrix bestimmen	确定矩阵的像和核的维数与基	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Gram-Schmidt - Ein Beispiel - (Gram-Schmidt'sches Orthonormalisierungsverfahren)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Lösungsmenge eines linearen Gleichungssystems bestimmen	确定线性方程组的解集	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Lineare Abbildungen - Beweis oder Gegenbeispiel?		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Unterraum? Beweis oder Gegenbeispiel?		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Riemann Integral vs. Lebesgue Integral	黎曼积分与勒贝格积分	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra - Part 2 (Logic, deduction rules)	线性代数 - 第二部分 (逻辑, 推理规则)	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Linear Algebra - Part 1 (Logic) [old version]	线性代数 - 第一部分 (逻辑) [旧版本]	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Aufgabe zum Satz von Stokes (Vektoranalysis Teil 25)	斯托克斯定理练习题（向量分析第25部分）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Substitution rule, transformation formula, change of variables		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Aufgabe zum Satz von Gauß (Vektoranalysis Teil 24)	高斯定理习题（向量分析第24部分）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Real Analysis - Numbers (a short overview)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstand Punkt zu Gerade berechnen		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Polar form of complex numbers - How to calculate?		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Grothendieck-Gruppe - Konstruktion	格罗滕迪克群 - 构造	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Matrix invertieren mit dem Gauß-Jordan-Verfahren	高斯-约旦法求矩阵逆	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Aufgabe zu orientierten Oberflächenintegralen (Vektoranalysis Teil 22)	关于定向曲面积分的习题 (向量分析第22部分)	The Bright Side of Mathematics - Videos	数学的美好一面 - 视频	The Bright Side of Mathematics	原始链接
Satz von Stokes - Integralsatz von Stokes in R^3 (Vektoranalysis Teil 21)	斯托克斯定理 - R^3中的积分定理（向量分析第21部分）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Change of basis - transformation matrices	基变换 - 变换矩阵	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Vollständige Induktion - Beispielrechnung	数学归纳法 - 示例	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Satz von Gauß - Integralsatz von Gauß in R^3 (Vektoranalysis Teil 20)	高斯定理 - R^3 中的高斯积分定理 (向量分析第 20 部分)	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Orientierte Oberflächenintegrale (Vektoranalysis Teil 19)	定向曲面积分 (向量分析第19部分)	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Komposition von surjektiven Abbildungen ist surjektiv	满射映射的复合是满射。	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Lineare Gleichungssysteme, überbestimmte und unterbestimmte Systeme	线性方程组，超定和欠定系统	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Maßtheorie - Teil 1 - Sigma-Algebra	测度论 - 第一部分 - Sigma代数	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Jordan-Normalform - Teil 1 - Überblick	约当标准形 - 第一部分 - 概述	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
QR-Zerlegung - quadratische Matrix	QR分解 - 方阵	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
LR-Zerlegung - Beispielrechnung	LR分解 - 示例计算	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Lineare Abbildungen - Darstellungsmatrizen	线性映射 - 表示矩阵	The Bright Side of Mathematics - Videos	数学的精彩一面 - 视频	The Bright Side of Mathematics	原始链接
Partielle Differentialgleichungen Teil 2 (Sprechweisen)	偏微分方程第二部分 (说法)	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Gram-Schmidt (Gram-Schmidt'sches Orthonormalisierungsverfahren)	格拉姆-施密特正交化方法	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Partielle Differentialgleichungen Teil 1 (Sprechweisen)	偏微分方程第一部分（术语表达）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Basiswechsel - Transformationsmatrizen - Koordinatenwechsel		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 18 (Aufgabe 23 - Graphenfläche, Flächeninhalt)	向量分析第18部分 (习题 23 - 曲面, 面积)	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 17 (Aufgabe 22 - Kugeloberfläche)	向量分析第17部分 (习题22 - 球面)	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Algebraische und geometrische Vielfachheit?	代数和几何重数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Matrix diagonalisierbar?		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
"Statistisch signifikant"? Eine kurze allgemeine Erklärung		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Griechische Buchstaben im Schnellkurs		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Bestimmung von Eigenwerten und Eigenvektoren einer Matrix	确定一个矩阵的特征值和特征向量	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Matrizen - normal, hermitesch, selbstadjungiert, unitär	矩阵 - 正规、埃尔米特、自伴、酉	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Eigenwerte einer Matrix	矩阵的特征值	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Satz von Baire	贝尔定理	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Topologie: Netze		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Komplexe Zahlen: Gleichungen lösen		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Komplexe Zahlen: Realteil und Imaginärteil bestimmen		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Determinantenformel für Blockmatrizen	分块矩阵的行列式公式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Riemann-Integral Definition		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 16 (Oberflächenintegral)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 15 (Aufgabe 21 - Graphenfläche)	向量分析第15部分（习题21 - 图形面积）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 14 (Aufgabe 19 - Zylinderoberfläche)	向量分析第14部分（习题19 - 圆柱面）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Riemann-Integral vs. Lebesgue-Integral	黎曼积分与勒贝格积分	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 13 (Aufgabe 18 - Kugeloberfläche)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 12 (Flächen im Raum)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 11 (Aufgabe 17 - Potentiale von Vektorfeldern)	矢量分析第11部分（习题17 - 矢量场的势）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Skalarprodukt	标量积	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Was ist eine Norm? Normierter Raum?	什么是规范规范化的空间	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 10 (Aufgabe 16 - Kurvenintegrale über Vektorfelder)	向量分析第10部分 (习题16 - 向量场上的曲线积分)	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 9 (Potentiale)		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 8 (Aufgabe 15 - Kurvenintegrale über Vektorfelder)	向量分析第8部分 (习题15 - 向量场的曲线积分)	The Bright Side of Mathematics - Videos	数学光明的一面 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 7 (Aufgabe 14 - Kurvenintegrale über Vektorfelder)	矢量分析第7部分（习题14 - 向量场的曲线积分）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 6 (orientierte Kurvenintegrale über Vektorfelder)	向量分析第6部分（关于向量场的定向曲线积分）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 5 (Aufgabe 13 - Kurvenintegrale)	向量分析第五部分（习题13 - 曲线积分）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 4 (Aufgabe 12 - Bogenlänge)	向量分析第4部分 (习题 12 - 弧长)	The Bright Side of Mathematics - Videos	数学的闪光点 - 视频	The Bright Side of Mathematics	原始链接
Vektoranalysis Teil 1 (Wege, parametrisierte Kurven, Bogenlänge, Tangentialvektor, Normalenvektor)	向量分析第一部分 (路径, 参数化曲线, 弧长, 切向量, 法向量)	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Mehrdimensionale Integration Teil 13 (Aufgabe 9 - Fläche der Astroide berechnen, Sternkurve)	多维积分第13部分（习题9 - 计算星形线面积，星形曲线）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Mehrdimensionale Integration Teil 1 (Satz von Fubini)	多维积分第一部分（富比尼定理）	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Lipschitz-Stetigkeit. Was sind Lipschitz-stetige Funktionen?		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abgeschlossene Mengen	闭集	The Bright Side of Mathematics - Videos	数学的明亮面 - 视频	The Bright Side of Mathematics	原始链接
Abbildungen und Funktionen	映射和函数	The Bright Side of Mathematics - Videos	数学的明亮一面 - 视频	The Bright Side of Mathematics	原始链接
Logarithmengesetze im Komplexen	复数中的对数法则	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Der Hilbertkubus bzw. Hilbertwürfel ist kompakt		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Das Argument der Diagonalfolge		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Offene Mengen	开集	The Bright Side of Mathematics - Videos	数学的光明一面 - 视频	The Bright Side of Mathematics	原始链接
Metrischer Raum		The Bright Side of Mathematics - Videos		The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 33 \| Extension of Determinant	抽象线性代数33 行列式的扩展	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Algebra 14 \| Cyclic Groups [dark version]	代数14 循环群【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Generating Conic Sections with Circles \| Part 3. The Hyperbola		Think Twice - Videos		Think Twice	原始链接
Generating Conic Sections with Circles \| Part 2. The Parabola		Think Twice - Videos		Think Twice	原始链接
Generating Conic Sections with Circles \| Part 1. The Ellipse		Think Twice - Videos		Think Twice	原始链接
Euler's Formula V - E + F = 2 \| Proof	欧拉公式 V - E + F = 2 证明	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Every Polygon can be Triangulated Into Exactly n-2 Triangles \| Proof by Induction	每个多边形都可以被三角剖分成恰好n-2个三角形通过归纳法证明	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Spherical Geometry: Deriving The Formula For The Area Of A Spherical Triangle	球面几何推导球面三角形面积公式	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
The Fermat Point of a Triangle \| Geometric construction + Proof \|	三角形的费马点几何构造与证明	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
A fun probability puzzle with a neat geometric solution.	一道有趣的概率谜题，其几何解法巧妙简洁。	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Constructing a Square of Equal Area to a given Polygon	构建与给定多边形面积相等的正方形	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Alternating series #2 \| Visual solution \|	交错级数 2 视觉解法	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Visual Calculus: Derivative of sin(θ) is cos(θ)	视觉微积分：sin(θ)的导数是cos(θ)	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
What is the area under an arc of a cycloid curve?	摆线曲线一段弧下的面积是多少	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Napoleon's theorem \| Proof \|	拿破仑定理的证明	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Cavalieri's Principle in 3D \| Volume of a sphere \|	卡瓦列里原理在三维空间中的应用——球体的体积	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Alternating series #1 \| Visual solution \|	交错级数1 视觉解法	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Pythagorean theorem \| 3 Visual Proofs \|	毕达哥拉斯定理 3种视觉证明	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Approximating Pi ( Monte Carlo integration ) \| animation	近似计算圆周率（蒙特卡洛积分法）动画	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Finding the general formula for nth octagonal number \| Visual proof \|	寻找第n个八边形数的一般公式视觉证明	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Arithmetic mean vs Geometric mean \| inequality among means \| visual proof	算术平均数与几何平均数的不等式平均数之间的比较视觉证明	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Infinite Sums \| Geometric Series \| Explained Visually	无限求和几何级数视觉化解析	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Geometry of Binomial Theorem \| Visual Representation \| 2 examples	二项式定理的几何解释视觉呈现 2个示例	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Four squares with constant area \| Visual Proof \| Squaring the segments \|	恒定面积四方形视觉证明线段平方化	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Geometry: Viviani's theorem \| Visualization + Proof \|	几何学维维亚尼定理可视化+证明	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Fitting a Cube Through a Copy of Itself \| Rupert's Cube \|	让立方体穿过自身的复制品鲁珀特立方体	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Chaos Game \| Fractals emerging from chaos \| Computer simulation \|	混沌游戏从混沌中涌现的分形计算机模拟	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Unfolding The Dragon \| Fractal Curve \|	展开龙形分形曲线	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Double pendulum \| Chaos \| Butterfly effect \| Computer simulation	双摆混沌蝴蝶效应计算机模拟	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Cutting a Möbius strip in half (and more) \| Animated Topology \|	将莫比乌斯带一分为二（及更多）动画拓扑学	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Area of dodecagon \| Beautiful geometry \| Visual mathematics	十二边形的面积美丽的几何视觉数学	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Sum of first n odd numbers \| Visual mathematics \|	前n个奇数之和视觉数学	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Beautiful visualization \| Sum of first n Hex numbers = n^3 \| animation	美丽可视化前n个六边形数之和等于n³ 动画	Think Twice - Videos	三思而行 - 视频	Think Twice	原始链接
Sum of n squares \| explained visually \|	n个平方和的视觉解释	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Nicomachus's theorem \| Visualisation \| 3-D animation \|	尼科马库斯定理可视化 3D动画	Think Twice - Videos	三思而后行 - 视频	Think Twice	原始链接
Lecture 1 – NLU Course Overview \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 2 – Word Vectors 1 \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 3 – Word Vectors 2 \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 4 – Word Vectors 3 \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 5 – Sentiment Analysis 1 \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 6 – Sentiment Analysis 2 \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 7 – Relation Extraction \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 8 – NLI 1 \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 9 – NLI 2 \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 10 – Grounding \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 11 – Semantic Parsing \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 12 – Evaluation Methods \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 13 – Evaluation Metrics \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 14 – Contextual Vectors \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
Lecture 15 – Presenting Your Work \| Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford CS224U: Natural Language Understanding \| Spring 2019		Stanford Online	原始链接
How to build an AI Agent — starting from scratch				Underfitted	原始链接
Stanford CS234 Reinforcement Learning I Introduction to Reinforcement Learning I 2024 I Lecture 1		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Tabular MDP Planning I 2024 I Lecture 2		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Policy Evaluation I 2024 I Lecture 3		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Q learning and Function Approximation I 2024 I Lecture 4		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Policy Search 1 I 2024 I Lecture 5		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Policy Search 2 I 2024 I Lecture 6		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Policy Search 3 I 2024 I Lecture 7		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Offline RL 1 I 2024 I Lecture 8		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 I Guest Lecture on DPO: Rafael Rafailov, Archit Sharma, Eric Mitchell I Lecture 9		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Offline RL 3 I 2024 I Lecture 10		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Exploration 1 I 2024 I Lecture 11		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Exploration 2 I 2024 I Lecture 12		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Exploration 3 I 2024 I Lecture 13		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Multi-Agent Game Playing I 2024 I Lecture 14		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Emma Brunskill & Dan Webber I 2024 I Lecture 15		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Stanford CS234 Reinforcement Learning I Value Alignment I 2024 I Lecture 16		Stanford CS234 I Reinforcement Learning I Spring 2024 I Emma Brunskill		Stanford Online	原始链接
Lecture 60: Optimizing Linear Attention	第六十讲优化线性注意力	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Lecture 59: FastVideo	第五十九讲快速视频	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Lecture 58: Disaggregated LLM Inference	第58讲分解式大型语言模型推理	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Lecture 57: CuTe	第57讲 CuTe	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Lecture 56: Kernel Benchmarking Tales	第五十六讲内核基准测试的故事	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Lecture 55: Modular’s unified device accelerator language	第55讲 Modular的统一设备加速语言	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Lecture 54: Small RL Models at the Speed of Light with LeanRL	第54讲利用LeanRL实现光速小型强化学习模型	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
GPU MODE @ GTC 2025	GPU模式@GTC 2025	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Bonus Lecture: AMD Developer Challenge	额外讲座 AMD开发者挑战赛	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Lecture 53: torch.compile Q&A	第53讲 torch.compile 问答	GPU MODE - Videos	GPU模式 - 视频	GPU MODE	原始链接
Summer of Math Exposition #4 \| Teachers, I'd love to hear from you	数学展示之夏4 老师们，我很想听听你们的想法	3Blue1Brown - Videos	3Blue1Brown - 视频	3Blue1Brown	原始链接
Where my explanation of Grover’s algorithm failed	我对Grover算法的解释在哪里失败了	3Blue1Brown - Videos	3Blue1Brown - 视频	3Blue1Brown	原始链接
But what is quantum computing? (Grover's Algorithm)	但什么是量子计算（格罗弗算法）	3Blue1Brown - Videos	3Blue1Brown - 视频	3Blue1Brown	原始链接
Something weird happens in dimension 8	在第八维度中发生了奇怪的事情	Aleph 0 - Videos	阿列夫0 - 视频	Aleph 0	原始链接
The surprising geometry of soap films	肥皂膜出人意料的几何形态	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Does Assembly Theory Explain Life? Let's do the math.	组装理论能解释生命吗？让我们来算一算。	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
The Math Behind Climate Models (in 4 levels of complexity)	气候模型背后的数学（四个复杂度层次）	Dr. Trefor Bazett - Videos	特雷弗·巴泽特博士 - 视频	Dr. Trefor Bazett	原始链接
Extraction of Roots of Complex Numbers	复数的根提取	MathTheBeautiful - Videos	MathTheBeautiful - 视频	MathTheBeautiful	原始链接
Fourier Transform 19 \| Proof of Pointwise Convergence of Fourier Series	傅里叶变换19：傅里叶级数的逐点收敛证明	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 18 \| Dirichlet Kernel [dark version]	傅里叶变换18 狄利克雷核【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 18 \| Dirichlet Kernel	傅里叶变换18 狄利克雷核	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 17 \| Pointwise Convergence of Fourier Series [dark version]	傅里叶变换17：傅里叶级数的逐点收敛【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 17 \| Pointwise Convergence of Fourier Series	傅里叶变换17 傅里叶级数的逐点收敛	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 37 \| Fitting Index [dark version]	抽象线性代数37 拟合指数【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 37 \| Fitting Index	抽象线性代数37 拟合指数	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 36 \| Generalized Eigenspaces [dark version]	抽象线性代数36 广义特征空间 [暗黑版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 36 \| Generalized Eigenspaces	抽象线性代数36 广义特征空间	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 35 \| Definition of Jordan Normal Form [dark version]	抽象线性代数35 约当标准形的定义【暗黑版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 35 \| Definition of Jordan Normal Form	《抽象线性代数35 约当标准形的定义》	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 24 \| Characteristic Polynomial [dark version]	常微分方程24 特征多项式 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 24 \| Characteristic Polynomial	常微分方程24 特征多项式	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 23 \| Example for Matrix Exponential [dark version]	常微分方程23 矩阵指数示例 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 23 \| Example for Matrix Exponential	常微分方程23 矩阵指数示例	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 22 \| Properties of the Matrix Exponential [dark version]	常微分方程22 矩阵指数的性质 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Ordinary Differential Equations 22 \| Properties of the Matrix Exponential	常微分方程22 矩阵指数的性质	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 34 \| Eigenvalues and Eigenvectors for Linear Maps [dark version]	抽象线性代数34：线性映射的特征值与特征向量【暗色版】	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Abstract Linear Algebra 34 \| Eigenvalues and Eigenvectors for Linear Maps	抽象线性代数34 线性映射的特征值与特征向量	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 44 \| Change of Variables [dark version]	流形44 变量变换 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Manifolds 44 \| Change of Variables	流形44 变量替换	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Fourier Transform 16 \| Calculating Sums with Fourier Series [dark version]	傅里叶变换16 用傅里叶级数求和 [暗色版]	The Bright Side of Mathematics - Videos	数学的光明面 - 视频	The Bright Side of Mathematics	原始链接
Workshop on_ Zero-Order Optimization(1)_video	零阶优化工作坊(1)_视频		0890f8cd	https://space.bilibili.com/1590402692/upload/video	原始链接
探索数学优化中基于学习的算法和理论_video	探索数学优化中基于学习的算法与理论视频		d09db9aa	https://space.bilibili.com/1590402692/upload/video	原始链接
矩阵单调优化_video	矩阵单调优化视频		7ce74c65	https://space.bilibili.com/1590402692/upload/video	原始链接
利用小尺寸 GNN 解决大规模线性规划问题：理论与应用_video	利用小尺寸GNN解决大规模线性规划问题：理论与应用视频		5724fe7f	https://space.bilibili.com/1590402692/upload/video	原始链接
整合多组学数据用于脑部疾病的预防、诊断和治疗_video	Integrating multi-omics data for the prevention, diagnosis, and treatment of brain disorders_video		d50dd6d9	https://space.bilibili.com/1590402692/upload/video	原始链接
揭示复杂系统的多稳定性：解决方案领域的新视野_video	揭示复杂系统的多稳定性：解决方案领域的新视野_视频		9fcac0b0	https://space.bilibili.com/1590402692/upload/video	原始链接
NeuroPrim_ 解决 NP 难生成树问题的通用学习模型_video	NeuroPrim_ 解决NP难生成树问题的通用学习模型_video		e8591791	https://space.bilibili.com/1590402692/upload/video	原始链接
“Mathematical Programming Computation” Seminar Series_ Prof. Thorsten Koch_video	“数学编程计算”研讨会系列_托尔斯滕·科赫教授_视频		fb668f61	https://space.bilibili.com/1590402692/upload/video	原始链接
Distributed Hypothesis Testing Over AWGN Channels_video	分布式假设检验在加性高斯白噪声信道上的应用_视频		6001d853	https://space.bilibili.com/1590402692/upload/video	原始链接
Certifiably Robust Learning via Knowledge-Enabled Logical Reasoning_video	《基于知识驱动逻辑推理的可验证鲁棒学习》_视频		eb3f44d6	https://space.bilibili.com/1590402692/upload/video	原始链接
Model Based Deep Learning_ Applications to Imaging and Communications_video	基于模型的深度学习：在成像与通信中的应用视频		0aa389cb	https://space.bilibili.com/1590402692/upload/video	原始链接
Workshop on_ Zero-Order Optimization(2)_video	零阶优化工作坊（2）_视频		bf5930b0	https://space.bilibili.com/1590402692/upload/video	原始链接
以极低的一位通信开销对大型模型进行全参数联合微调_video	以极低的通信开销实现大型模型全参数联合微调		f2357e11	https://space.bilibili.com/1590402692/upload/video	原始链接
Multi-IRS Multi-Reflection Beam Routing for Future Wireless Networks_ Performan_video	未来无线网络中的多IRS多反射波束路由：性能视频		50a56c70	https://space.bilibili.com/1590402692/upload/video	原始链接
Academical AI Research @ Post-GPT Era_video	后GPT时代的学术AI研究_视频		594a6736	https://space.bilibili.com/1590402692/upload/video	原始链接
Evaluating Optimization Software_video	评估优化软件_视频		（注：原文“fa2fc2da”看起来像是一串随机字符或编码，没有实际语义内容，因此直译为相同形式。） fa2fc2da	https://space.bilibili.com/1590402692/upload/video	原始链接
Interactive Language Models with Memory_video	带记忆的交互式语言模型视频		c919befa	https://space.bilibili.com/1590402692/upload/video	原始链接
Will AI Destroy or Reinvent Education?	人工智能会摧毁还是重塑教育	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Tim Cook Tells Apple Staff "AI Is Ours To Grab"	蒂姆·库克告诉苹果员工"AI机遇由我们把握"	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Is GPT-OSS Actually Any Good?	GPT-OSS真的靠谱吗	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
The AI Model Wars Just Heated WAY Up	人工智能模型大战骤然升温	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻 - 视频版》	The AI Daily Brief: Artificial Intelligence News	原始链接
AI Is Making Oodles Of Money	人工智能正在赚大钱	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻 - 视频版》	The AI Daily Brief: Artificial Intelligence News	原始链接
Can AI Trade Stocks?	人工智能能炒股吗	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Microsoft is Feeling the AGI	微软正感受到通用人工智能（AGI）的存在	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻 - 视频版》	The AI Daily Brief: Artificial Intelligence News	原始链接
How One Company Saved 213,000 Hours with AI	一家公司如何用AI节省21.3万小时	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻 - 视频版》	The AI Daily Brief: Artificial Intelligence News	原始链接
5 Uses for the new ChatGPT Agent	新ChatGPT代理的五大用途	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Will Apple Buy Mistral?	苹果会收购Mistral吗	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
The Latest on Fair Use in AI Training	人工智能训练中合理使用的最新进展	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Anthropic Starts Tracking AI's "Economic Fallout"	Anthropic开始追踪人工智能的"经济余波"	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
How the War for Talent Will Shape AI	人才争夺战将如何塑造人工智能	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Agent Deployments Tripled Last Quarter	上季度代理部署数量增长三倍	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频集锦》	The AI Daily Brief: Artificial Intelligence News	原始链接
Goldman Says Market Was Wrong About Deepseek	高盛称市场对深度求索的看法有误	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Should AI Mean a 4 Day Workweek?	人工智能是否意味着每周四天工作制	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Everything is Now a Vibe Coding App	万物皆成氛围编码应用	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻 - 视频集锦》	The AI Daily Brief: Artificial Intelligence News	原始链接
MCP and Observability Come to Agentforce 3.0	MCP与可观测性功能融入Agentforce 3.0	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Context Engineering: What It Is and Why It Matters	情境工程学：概念解析及其重要性	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
The Quest for the One-Person One-Billion Dollar Company	追寻一人十亿美元企业的梦想	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Can Buying Perplexity Save Apple on AI?	购买Perplexity能否拯救苹果的人工智能	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
3 Ways To Get Better At AI Right Now	立即提升AI技能的3种方法	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
AI Engineering & Research Offers Hit $100M	AI工程与研究报价突破1亿美元	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
10 AI Video Trends Taking Over the Internet	10大AI视频趋势席卷互联网	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
It's Settler's of Catan But With AI Companies	这是《卡坦岛》的AI公司版	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
20+ New Jobs that AI Will Create	人工智能将创造的20多个新岗位	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Should You Build Single Agents or Multi Agent Systems?	你应该构建单一代理还是多代理系统	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
16 Ways Enterprise AI is Changing	企业AI变革的16种方式	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Why Your Company Needs to Move Faster on AI	为何您的公司需加速推进人工智能应用	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻 - 视频版》	The AI Daily Brief: Artificial Intelligence News	原始链接
How This Totally Unhinged AI Ad Shows the Future of Advertising	这段完全失控的AI广告如何预示广告业的未来	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
OpenAI's Open Model Gets Delayed	OpenAI的开放模型发布推迟	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Is Meta's Scale Acquisition About Cutting Off AI Data to Competitors?	Meta的大规模收购是为了切断竞争对手的AI数据吗	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
What's the Bigger Deal for AI: 3 Pro or o3 80% Price Drop?	AI 3 Pro与o3降价80%，哪个更值得关注？	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
The Illusion of [Good] Thinking: Why You Can Safely Ignore Apple's New AI Paper	[良好]思维的幻觉为何你可以放心忽略苹果的新AI论文	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
How to Design an AI Native Engineering Organization	如何设计一个原生AI工程组织	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
The Fastest Growing Software Companies Right Now Are All Agents	目前增长最快的软件公司都是代理商	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻 - 视频版》	The AI Daily Brief: Artificial Intelligence News	原始链接
In AI Era, Human Customer Service is VIP	在AI时代，人工客服才是VIP	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Why AI Skeptics Are Nuts	为何对人工智能持怀疑态度的人大错特错	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
AI Infiltrates Search	人工智能渗透搜索领域	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Checking In on the AI First Companies	关注AI先行企业	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
Anthropic Gets Voice Mode	Anthropic推出语音模式	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接
The Biggest Trends from the AI Engineer World's Fair	AI工程师世界博览会上的最大趋势	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻 - 视频版》	The AI Daily Brief: Artificial Intelligence News	原始链接
Does 'AI First' Mean "AI Replacing People?	“AI优先”是否意味着“AI取代人类”	The AI Daily Brief: Artificial Intelligence News - Videos	《AI每日简报：人工智能新闻与视频》	The AI Daily Brief: Artificial Intelligence News	原始链接

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